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Computational methods of linear algebra. (English) Zbl 0451.65015

MSC:
65Fxx Numerical linear algebra
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
00A15 Bibliographies for mathematics in general
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[1] A. A. Abramov, ?Some remarks on finding the eigenvalues and eigenvectors of matrices arising in the application of the Ritz method and the method of grids,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 3, 644?647 (1967).
[2] A. A. Abramov, ?Ideas of permutation theory in some algorithms of linear algebra,? in: Modern Numerical Methods, No. 1 (Materials of the International Summer School on Numerical Methods, Kiev, 1966), Moscow (1968), pp. 85?101.
[3] V. I. Agoshkov and Yu. A. Kuznetsov, ?The Lanczos method in eigenvalue problems,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1972), pp. 145?164.
[4] I. Ya. Akushskii and Yu. G. Zolotarev, ?On a method of solving systems of linear algebraic equations,? Elektron. Tekhnika. Nauch. Tekh. Sb. Mikroelektronika,4 (30), 87?89 (1971).
[5] M. A. Aleksidze, ?On a method of inverting symmetric matrices,? Dokl. Akad. Nauk SSSR,191, No. 3, 507?510 (1970).
[6] L. P. Andreeva, ?On practical application of the orthogonal power method,? in: Computational Methods and Programming. No. 3, Moscow State Univ. (1965), pp. 61?68.
[7] L. P. Andreeva, ?On the realization of the P-algorithm,? in: Computational Methods and Programmings No. 8, Moscow State Univ. (1967), pp. 243?247.
[8] A. S. Apartsin and Ten Men Yan, ?Solution of poorly conditioned systems of linear algebraic equations by means of a priori smoothing,? in: Some Questions of Optimization and Control in Energy Systems [in Russian], Irkutsk (1972), pp. 24?27.
[9] V. S. Apokorina and V. I. Lebedev, ?On the application of the method of inverse iterations in limiting cases,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 23?33.
[10] Yu. Akhatov and A. Umirbekov, ?Solution of a system of linear algebraic equations by Monte Carlo methods,? Tr. Tashkent. Politekh. Inst.,76, 74?89 (1972).
[11] V. A. Baklanova, ?Generalization of the method of deflation,? Nauch. Tr. Tashkent. Univ.,276, 14?19 (1966).
[12] V. A. Baklanova, ?On the refinement of an eigenvalue and an eigenvector of a matrix,? Nauch. Tr. Tashkent. Univ.,276, 20?23 (1966).
[13] V. A. Baklanova, ?On refinement of an eigenvalue and an eigenvector of a matrix,? Nauch. Tr. Tashkent. Univ.,316, 55?60 (1968).
[14] A. B. Bakushinskii, ?A method of solving ?degenerate? and ?almost degenerate? linear algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,3, No. 6, 1113?1114 (1964).
[15] A. N. Baluev and M. K. Gavurin, ?Experiments on regularization of difference schemes,? in: Computational Methods [in Russian], No. 5, Leningrad State Univ. (1968), pp. 14?18.
[16] N. S. Bakhvalov, Numerical Methods. Vol. 1, Analysis, Algebra, Ordinary Differential Equations [in Russian], Nauka, Moscow (1973). · Zbl 0263.34042
[17] A. Ya. Belostotskii, ?On an estimate of the quality of approximate solutions of a system of linear algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 1, 112?114 (1965).
[18] Yu. F. Belousov, ?On a method of inverting matrices,? in: Materials of the 27th Interschool Conference of Mathematics Departments of the Pedagogical Institutes of the Ural Zone [in Russian], Izhevsk (1969), pp. 159?161.
[19] I. S. Berezin and N. P. Zhidkov, Method of Computations [in Russian], Vol. 1, 3rd ed., Nauka, Moscow (1966).
[20] S. T. Bersenev, A. L. Deinezhenko, and N. I. Sablin, ?A numerical algorithm for finding an approximate I. pseudosolution for systems of linear algebraic equations,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 86?94.
[21] Yu. V. Blagoveshchenskii and L. D. Nikolenko, ?On refinement of the eigenvalues and eigenvectors in the case of multiple roots of the characteristic equation,? Dopovidi Akad. Nauk Ukr. RSR, No. 6, 699?702 (1966).
[22] A. N. Bogolyubov and V. I. Telegin, ?On a numerical method of solving linear systems of equations with a tridiagonal matrix,? Zh. Vychisl. Mat. Mat. Fiz.,14, No. 3, 768?771 (1974). · Zbl 0283.65009
[23] K. Boyadzhiev, ?The inverse matrix of three-term systems of equations,? in: Investigations in the Theory of Construction [in Russian], No. 1.4, Stroiizdat, Moscow (1965), pp. 253?258.
[24] Yu. E. Boyarintsev and Zh.L.Korobitsina, ?Construction of a convergent multistep iterative process,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1969), pp. 11?15.
[25] A. L. Brudno, ??-solutions of linear algebraic systems,? in: Problems of Cybernetics [in Russian], No. 8, Fizmatgiz, Moscow (1962), pp. 187?190.
[26] V. A. Bulavskii, ?On the decomposition of square matrices into the product of an orthogonal and triangular matrix,? Sib. Mat. Zh.,10, No. 2, 467?469 (1969). · Zbl 0196.05701 · doi:10.1007/BF00970445
[27] V. Ya. Bulygin and P. G. Danilaev, ?On the question of determining hydroconductivity by solving a poorly conditioned system of linear algebraic equations,? in: Numerical Methods in Technology-Economics Problems [in Russian], Kazan Univ., Kazan (1971), pp. 15?18.
[28] B. Bukhberger and G. A. Emel’yanenko, ?Methods of inverting tridiagonal matrices,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 3, 546?554 (1973).
[29] W. Wasow and G. Forsythe, Difference Methods for Solving Partial Differential Equations [Russian translation], IL, Moscow (1963). · Zbl 0108.29803
[30] V. V. Voevodin, ?Solution of the full eigenvalue problem by power methods,? in: Computational Methods and Programming [in Russian], No. 3, Moscow State Univ. (1965), pp. 7?54.
[31] V. V. Voevodin, ?Stability of power methods,? in: Computational Methods and Programming [in Russian], No. 3, Moscow State Univ. (1965), pp. 55?60.
[32] V. V. Voevodin, ?Solution of the full eigenvalue problem by the method of rotations,? in: Computational Methods and Programming [in Russian], No. 3, Moscow State Univ. (1965), pp. 89?105.
[33] V. V. Voevodin, Numerical Methods of Algebra. Theory and Algorithms [in Russian], Nauka, Moscow (1966).
[34] V. V. Voevodin, ?On the order of eliminating unknowns,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 4, 758?760 (1966).
[35] V. V. Voevodin, ?On the asymptotic distribution of rounding errors in linear transformations,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 5, 965?976 (1967).
[36] V. V. Voevodin, ?Orthogonal transformations in linear algebra,? in: Modern Numerical Methods, No. 1 (Materials of the International Summer School on Numerical Methods, Kiev, 1966), Moscow (1968), pp. 3?15.
[37] V. V. Voevodin, ?Orthogonal transformations and the solution of systems of equations with rectangular matrices,? in: Rounding Errors in Algebraic Processes, Moscow State Univ. (1968), pp. 39?58.
[38] V. V. Voevodin, ?On the accuracy of solving systems of equations by direct methods,? Zh. Vychisl. Mat. Mat. Fiz.,8, No. 5, 1094?1096 (1968).
[39] V. V. Voevodin, Rounding and Stability in Direct Methods of Linear Algebra [in Russian], Moscow State Univ. (1969).
[40] V. V. Voevodin, ?On a method of regularization,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 3, 673?675 (1969).
[41] V. V. Voevodin, ?On the asymptotic distribution of rounding errors in the decomposition of a matrix into factors and in solving systems of equations,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 4, 932?934 (1969).
[42] V. V. Voevodin, ?Development of methods of solving problems in the University Computer Center,? Vestn. Mosk. Gos. Univ., No. 2, 69?82 (1970).
[43] V. V. Voevodin, ?On a programming packet for problems of linear algebra,? in: Mathematical Provision for the Computer [in Russian], Kiev (1972), pp. 107?108.
[44] V. V. Voevodin (ed.), Numerical Analysis in FORTRAN, Nos. 1, 2, 3, 6, 9, Moscow State Univ. (1973?1974).
[45] V. V. Voevodin and V. M. Volovich, ?On solving systems with many right sides,? Zh. Vychisl. Mat. Mat. Fiz.,10, No. 4, 1025?1027 (1970).
[46] V. V. Voevodin and V. M. Volovich, ?On the choice of principal cell in the cell versions of the Gauss method for solving systems of linear algebraic equations,? in: Computational Methods and Programming [in Russian], No. 18, Moscow State Univ. (1972), pp. 188?192.
[47] V. V. Voevodin and V. M. Volovich, ?Solution of the eigenvalue problem for a tridiagonal matrix in the packet of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 3, Moscow State Univ. (1973), pp. 114?151.
[48] V. V. Voevodin and Kh. D. Ikramov, ?On an extension of the Jacobi method,? in: Computational Methods and Programming [in Russian], No. 8, Moscow State Univ. (1967), pp. 216?228.
[49] V. V. Voevodin, N. A. Ismailova, L. I. Karysheva, G. D. Kim, R. V. Petrina, and I. V. Chepurina, ?General macromodules generated by problems of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 2, Moscow State Univ. (1973), pp. 19?114.
[50] V. V. Voevodin, L. I. Karysheva, G. D. Kim, and R. V. Petrina, ?A complex of algorithms based on reflection transformations in the packet of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 3, Moscow State Univ. (1973), pp. 6?49.
[51] V. V. Voevodin and G. D. Kim, ?Principles of constructing a packet for the solution of problems of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 2, Moscow State Univ. (1973), pp. 5?18.
[52] V. V. Voevodin, G. D. Kim, L. I. Karysheva, and Z. I. Agafonova, ?The QR algorithm for solving the full eigenvalue problem for a matrix of general form,? in: Numerical Analysis in FORTRAN [in Russian], No. 9, Moscow State Univ. (1974), pp. 36?86.
[53] V. V. Voevodin and R. V. Petrina, ?A complex of algorithms based on transformations of Gauss type in the packet of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 3, Moscow State Univ. (1973), pp. 50?96.
[54] V. V. Voevodin and T. L. Rudneva, ?On a cell version of the reflection method in solving linear algebraic systems,? Zh. Vychisl. Mat. Mat. Fiz.,10, No. 5, 1281?1285 (1970). · Zbl 0212.17004
[55] S. N. Voevodina, ?A complex of algorithms connected with cellular Toeplitz matrices in the packet of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 9, Moscow State Univ. (1974), pp. 115?131.
[56] V. M. Volovich, ?On the solution of systems of linear algebraic equations by cell methods,? in: Computational Methods and Programming [in Russian], No. 3, Moscow State Univ. (1965), pp. 106?133.
[57] V. M. Volovich, ?On the solution of systems of linear algebraic equations of high order on machines with small operative memory,? in: Computational Methods and Programming [in Russian], No. 8, Moscow State Univ. (1967), pp. 229?242. · Zbl 0229.65041
[58] Yu. V. Vorob’ev, ?A random iterative process,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 6, 1088?1093 (1964).
[59] Yu. V. Vorob’ev, ?A random iterative process. II,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 5, 787?795 (1965).
[60] Yu. V. Vorob’ev, ?A random iterative process in the method of variable directions,? Zh. Vychisl. Mat. Mat. Fiz.,8, No. 3, 663?670 (1968).
[61] Yu. V. Vorob’ev and G. S. Medvedev, ?On the inversion of matrices of special type,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 2, 406?408 (1967).
[62] B. D. Vulichevich, ?On a method of inverting matrices,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,18, 96?103 (1970).
[63] B. D. Vulichevich, ?On inversion of rectangular matrices decomposed into blocks,? Math. Balkan.,3, 600?604 (1973).
[64] B. D. Vulichevich and V. N. Kublanovskaya, ?On the solution of the partial eigenvalue problem for certain matrices of special type,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,18, 104?115 (1970).
[65] A. Z. Gamm, ?On the solution of linear equations of high order with topologically symmetric matrices,? in: Methods of Control by Large Systems [in Russian], Vol. 2, Irkutsk (1970), pp. 211?219.
[66] F. R. Gantmacher, Theory of Matrices, Chelsea Publ. · Zbl 0085.01001
[67] I. F. Garchenyuk, ?Comparison of two algorithms for solving systems of linear algebraic equations,? in: Materials of the Fourth Republic Scientific Conference of Young Investigators in Systems Technology [in Russian], Vol. 2, Kiev (1969), pp. 81?84.
[68] I. F. Garchenyuk and V. V. Ivanov, ?Analysis of accuracy and comparison of some computational algorithms of linear algebra,? in: Questions of Accuracy and Effective Computational Algorithms, Proc. of a Symp., Vol. 1, Kiev (1969), pp. 16?27.
[69] I. M. Gel’fand, Lectures on Linear Algebra [in Russian], 4th Ed., Nauka, Moscow (1971).
[70] V. D. Glushenkov, ?On the sweep-out method for solving systems of linear algebraic equations with a (2k+1)-diagonal matrix,? in: Application of Method of Computational Mathematics and Computers in Technology-Economics Calculations [in Russian], No. 2, Kazan, Univ. (1970), pp. 134?136.
[71] V. S. Godlevskii, ?On an estimate of the accuracy of solutions of certain systems of linear algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 1, 233?237 (1973).
[72] V. S. Godlevskii, ?On estimates of the distribution laws of errors in solutions of systems of linear algebraic and ordinary differential equations,? Zh. Vychisl. Mat. Mat. Fiz.,14, No. 5, 1083?1092 (1974).
[73] V. K. Gordovskii, ?Use of a priori estimates of errors in solving systems of equations of high order,? in: Systems and Methods of Automatic Control [in Russian], Kiev (1970), pp. 5?12.
[74] V. I. Gordonova, ?Estimates of rounding errors in solving systems of conditional equations,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 4, 775?782 (1969).
[75] V. I. Gordonova, ?On the question of justifying algorithms for the choice of the regularization parameter,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 5, 1328?1332 (1973).
[76] V. I. Gordonova and V. A. Morozov, ?Numerical algorithms for choosing the parameter in the method of regularization,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 3, 539?545 (1973).
[77] V. I. Gordonova and V. A. Morozov, ?A subprogram for solving systems of linear algebraic equations by the method of regularization with a given error level,? in: Numerical Analysis in FORTRAN [in Russian], No. 6, Moscow State Univ. (1974), pp. 3?7.
[78] O. A. Goryachev, ?On the solution on a computer of systems of algebraic equations of high order,? Tr. Kuibyshev. Aviats. Inst.,54, 120?126 (1971).
[79] Sh. M. Gofman and T. S. Sadetov, ?On the question of improving the condition of the coefficient matrix of a system of linear algebraic equations,? Tr. Tashkent. Inst. Inzh. Zh.-D. Transp.,85, 3?11 (1972).
[80] A. B. Gribov, ?A method of recurrent computation of the characteristic polynomial,? Dokl. Akad. Nauk SSSR,177, No. 3, 499?500 (1967). · Zbl 0207.15702
[81] B. Griva, ?On the propagation of rounding errors in solving linear algebraic systems by the method of unique division,? Uch. Zap. Latv. Gos. Univ., Tr. Vychisl. Tsentra,58, No. 2, 257?263 (1964).
[82] G. M. Gusak and V. K. Kravtsov, ?On the computation of determinants in systems of residue classes,? in: Theory and Application of Mathematical Machines [in Russian], Belorussian State Univ., Minsk (1972), pp. 44?48.
[83] D. F. Davidenko, ?On the application of the method of variation of parameters to the computation of the associated matrix and its determinant,? Ukr. Mat. Zh.,17, No. 3, 59?66 (1965). · Zbl 0156.03404 · doi:10.1007/BF02527360
[84] D. F. Davidenko, ?On the approximate computation of determinants,? Ukr. Mat. Zh.,17, No. 5, 14?27 (1965). · Zbl 0196.47901 · doi:10.1007/BF02527083
[85] D. F. Davidenko, ?On the application of the method of variation of parameters to the construction of iterative formulas for increased accuracy for determining the elements of the inverse matrix,? Dokl. Akad. Nauk SSSR,162, No. 4, 743?746 (1965). · Zbl 0142.11405
[86] D. F. Davidenko, ?On an iterative method of variation of parameters for inversion of linear operations,? Inst. Atom. Energii im. I. V. Kurchatova, Preprint IAE-1963, Moscow (1970).
[87] D. F. Davidenko, ?On a class of iterative methods of third order for inverting linear operations,? Inst. Atom. Energ. im. Kurchatova, Preprint, IAE-2220, Moscow (1972).
[88] V. A. Daugavet, ?On a version of the graduated power method for finding several first eigenvalues of a symmetric matrix,? Zh. Vychisl. Mat. Mat. Fiz.,8, No. 1, 158?165 (1968).
[89] K. Dzhumaev, ?Comparative analysis of methods of solving poorly conditioned linear algebraic systems on the basis of numerical experiment,? in: Optimization and Organization of Computations [in Russian], Kiev (1972), pp. 62?70.
[90] S. Z. Dinkevich and I. R. Dovgard, ?On a method of inverting matrices,? in: The Finite Element Method and Structural Mechanics [in Russian], Leningrad (1974), pp. 201?203.
[91] A. P. Domoryad, ?On refining an eigenvalue and eigenvector of a matrix,? Nauch. Tr. Tashkent. Univ.,245, 8?10 (1964).
[92] A. M. Dubnov, ?Solution of a system of linear equations by matrix sweep-out,? Tr. Ts NII Stroit. Konstruktsii,9, 68?74 (1970).
[93] E. G. D’yakonov, ?On some iterative methods of solving systems of difference equations arising in the solution of partial differential equations of elliptic type by the method of grids,? in: Computational Methods and Programming [in Russian], No. 3, Moscow State Univ. (1965), pp. 191?222.
[94] E. G. D’yakonov, ?On the construction of iterative methods based on using spectrally equivalent operators,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 1, 12?34 (1966).
[95] E. G. D’yakonov, ?Interative methods of solving difference analogues of boundary value problems for equations of elliptic type,? in: Modern Computational Methods [in Russian], No. 4 (Materials of the International Summer School on Numerical Methods, Kiev, 1966), Kiev (1970).
[96] E. G. D’yakonov, Difference Methods of Solving Boundary Value Problems [in Russian], Moscow State Univ. (1971).
[97] I. V. Emelin, M. A. Krasnosel’skii, and N. P. Panskikh, ?The spurt method of constructing successive approximations,? Dokl. Akad. Nauk SSSR,219, No. 3, 535?538 (1974). · Zbl 0318.65012
[98] A. K. Emel’yanov, ?On a modified gradient method for solving systems of linear equations,? in: Methods and Models of Control [in Russian], No. 1, Riga (1971), pp. 73?76.
[99] M. I. Zhaldak and B. S. Kovbasenko, ?On an iterative process for finding the Chebyshev point of a system of linear equations,? Vychisl. Prikl. Mat., Mezhved. Nauch. Sb.,5, 104?111 (1968). · Zbl 0205.17201
[100] N. P. Zhidkov, ?Several remarks on the condition of systems of linear algebraic equations,? Zh. Vychisl. Mat. Fiz.,3, No. 5, 803?811 (1963).
[101] E. L. Zhukovskii, ?Statistical regularization of systems of algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 1, 185?191 (1972).
[102] E. L. Zhukovskii, ?On application of statistical regularizing algorithms to solving certain types of incorrectly posed problems,? in: Some Questions of Automation, Processing, and Interpretation of Physical Experiments [in Russian], No. 1, Moscow State Univ. (1973), pp. 133?169.
[103] E. L. Zhukovskii and P. N. Zaikin, ?On a numerical algorithm for finding quasisolutions of conditional systems of algebraic equations,? in: Some Questions of Automation, Processing, and Interpretation of Physical Experiments [in Russian], No. 2, Moscow State Univ. (1973), pp. 117?123.
[104] E. L. Zhukovskii and R. Sh. Liptser, ?On a recurrent method of computing normal solutions of linear algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 4, 843?857 (1972).
[105] E. L. Zhukovskii and V. A. Morozov, ?On sequential Bayes regularization of algebraic systems of equations,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 2, 464?465 (1972).
[106] A. F. Zabolotskaya, ?A method of accelerating convergence of an iterative method of determining the leading eigenvalue of a self-adjoint operator,? Zh. Vychisl. Mat. Mat. Fiz.,8, No. 3, 658?660 (1968).
[107] R. A. Zvyagina, ?On decomposition of a matrix with block structure into the product of matrices of triangular type,? Sb.Tr. Inst. Mat. Sib. Otd. Akad. Nauk SSSR,5 (22), 73?86 (1972).
[108] R. Zelinskii, ?Solution of a system of linear algebraic equations by the method of random search with parabolic interpolation,? Avtom. Vychisl. Tekh., No. 1, 88?89 (1980).
[109] O. V. Zenkin, ?Some remarks on the stability of the method of simple iteration,? in: Nauk. Prats’Aspirantiv, Kiivs’k. Univ. Fiz.-Mat., Kiev (1963), pp. 117?124.
[110] O. V. Zenkin, ?Some remarks on actual realization of the method of simple iterations,? in: Kibern. Tekh. Vychisl., Naukova Dumka, Kiev (1964), pp. 163?171.
[111] O. V. Zenkin, ?Some remarks on the stability of iterative processes,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 4, 745?748 (1964).
[112] A. V. Ivanov, ?Computational properties of regular difference equations,? Tr. Mat. Inst. Akad. Nauk SSSR,70, 59?115 (1964).
[113] V. V. Ivanov, ?On algorithms of optimal accuracy for solving linear algebraic systems on a computer,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 63?76.
[114] Kh. D. Ikramov, ?On representations of matrix norms,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 6, 1378?1383 (1969).
[115] Kh. D. Ikramov, Matrix Norms and Methods of Jacobi Type [in Russian], Moscow State Univ. (1969).
[116] Kh. D. Ikramov, ?The generalized method of rotations in the packet of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 3, Moscow State Univ. (1973), pp. 163?172.
[117] Kh. D. Ikramov and N. V. Petri, ?On the consistency of vector and matrix norms,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 5, 987?995 (1969).
[118] V. P. Il’in, ?On explicit schemes of variable directions,? Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Tekh.,13, No. 3, 97?104 (1967).
[119] V. P. Il’in, ?On certain estimates for methods of conjugate gradients,? Vychisl. Tsentr Sib. Otd. Akad. Nauk SSSR, Seminar Vychisl. Metody Prikl. Mat., No. 1, Preprint, Novosibirsk (1974).
[120] A. G. Ilyukhin, S. F. Feshchenko, E. S. Gavrilova, ?On a method of solving the eigenvalue problem for matrices,? Vychisl. Prikl. Mat., Mezhved. Nauch. Sb.,11, 16?25 (1970).
[121] N. A. Ismailova and M. A. Smirnova, ?On the distribution of rounding errors for linear transformations of vectors defined in the unit cube,? in: Rounding Errors in Algebraic Processes [in Russian], Moscow State Univ. (1968), pp. 25?28.
[122] L. I. Karysheva, ?A generalized eigenvalue problem,? in: Numerical Analysis in FORTRAN [in Russian], No. 9, Moscow State Univ. (1974), pp. 87?114.
[123] V. L. Katkov, ?On an improved matrix factorization,? Sib. Mat. Zh.,6, No. 3, 697?699 (1965).
[124] I. S. Kats, ?On the question of the rate of convergence of the method of successive relaxation,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 5, 996?1003 (1969).
[125] G. D Kim, ?On the solution of certain systems of linear algebraic equations of higher order,? in: Vychisl. Metody i Programmir., No. 3, Moscow State Univ. (1965), pp. 134?146.
[126] G. D. Kim, ?On the reduction of a system of linear equations to a form convenient for simple iteration,? in: Computational Methods and Programming [in Russian], No. 8, Moscow State Univ. (1967), pp. 248?253.
[127] G. D. Kim, ?On the statistical investigation of rounding errors in solving systems of linear algebraic equations by iterative methods,? in: Rounding Errors in Algebraic Processes [in Russian], Moscow State Univ. (1968), pp. 74?102.
[128] G. D. Kim, ?On the statistical investigation of rounding errors in solving systems of linear equations by iterative methods,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1969), pp. 90?91.
[129] G. D. Kim, ?On the statistical investigation of rounding errors of some algebraic transformations,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 3, 679?684 (1969).
[130] G. D. Kim, On the Distribution of Rounding Errors of Iterative Methods of Solving Systems of Linear Algebraic Equations [in Russian], Moscow State Univ. (1969).
[131] G. D. Kim, ?On statistical models of investigating rounding errors in problems of linear algebra,? in: Computational Methods and Programming [in Russian], No. 18, Moscow State Univ. (1972), pp. 173?187.
[132] G. D. Kim, ?Solution of the full eigenvalue problem for a Hermitian matrix by the method of rotation in the packet of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 3, Moscow State Univ., 97?113.
[133] G. D. Kim and I. V. Chepurina, ?Iterative refinement of an approximate solution of a system of linear algebraic equations,? in: Numerical Analysis in FORTRAN [in Russian], No. 9, Moscow State Univ. (1974), pp. 6?20.
[134] V. V. Klyuev and N. I. Kokovkin-Shcherbak, ?On minimization of the number of arithmetic operations in solving linear algebraic systems of equations,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 1, 21?33 (1965).
[135] V. V. Klyuev and N. I. Kokovkin-Shcherbak, ?On minimization of the number of operations in one transformation of a matrix,? Ukr. Mat. Zh.,18, No. 6, 122?128 (1966).
[136] V. V. Klyuev and N. I. Kokovkin-Shcherbak, ?On minimization of computational algorithms in certain matrix transformations,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 1, 3?13 (1967).
[137] G. G. Kovalenko, ?Application of the alternating method of Schwarz to the solution of systems of linear algebraic equations,? Dopovidi Akad. Nauk Ukr. RSR,A, No. 5, 410?415 (1967).
[138] A. B. Kovrigin, ?Estimate of the rate of convergence of a k-step gradient method,? Vestn. Leningr. Gos. Univ., No. 13, 34?36 (1970). · Zbl 0293.65032
[139] N. I. Kokovkin-Shcherbak, ?On minimization of computational algorithms for solving problems of elimination,? Zh. Vychisl. Mat. Mat. Fiz.,8, No. 5, 1096?1101 (1968).
[140] N. I. Kokovkin-Shcherbak, ?On minimization of computational algorithms for solving arbitrary systems of linear equations,? Ukr. Mat. Zh.,22, No. 4, 494?502 (1970).
[141] V. P. Kolomiets, ?On the solution of quasiband systems of linear algebraic equations by the method of group relaxation,? Uch. Zap. Tsentr. Aerogidrodinam. Inst.,2, No. 1, 92?102 (1971).
[142] V. N. Kostarchuk and B. P. Pugachev, ?A precise estimate of reducing error in a single step of the method of fastest descent,? Tr. Sem. po Funktsion. Anal., Voronezhsk. Univ., No. 2, 25?30 (1965).
[143] V. A. Kostrov, ?An algorithm for solving a system of algebraic equations of high order,? in: Control and Information [in Russian], No. 3, Vladivostok (1973), pp. 155?159.
[144] V. P. Kochergin and Yu. A. Kuznetsov, ?On the solution of systems of linear equations by the splitting method,? in: Computing Methods in the Theory of Transport [in Russian], Atomizdat, Moscow (1969), pp. 75?96.
[145] M. V. Krasikova, ?On the question of the choice of an effective method of solving systems of equations of of high order,? Izv. Vyssh. Uchebn. Zaved., Geod. Aerofotos ?emka, No. 3, 57?61 (1969).
[146] M. A. Krasnosel’skii and V. Ya. Stetsenko, ?Remarks on the Seidel method,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 1, 177?182 (1969).
[147] T. P. Krasulina, ?The method of stochastic approximation for determining the smallest eigenvalue of a symmetric matrix,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 6, 1383?1387 (1969).
[148] V. N. Kublanovskaya, ?On a method of reorthogonalization of a system of vectors,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 2, 338?340 (1964).
[149] V. N. Kublanovskaya, ?Reduction of an arbitrary matrix to tridiagonal form,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 3, 544 (1964).
[150] V. N. Kublanovskaya, ?On a computational scheme for the Jacobi process,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 4, 732?733 (1964).
[151] V. N. Kublanovskaya, ?Some estimates for the eigenvalues of a positive-definite matrix,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 1, 107?111 (1965).
[152] V. N. Kublanovskaya, ?On a process of orthogonalization of a system of vectors,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 2, 326?329 (1965).
[153] V. N. Kublanovskaya, ?An algorithm for the computation of the eigenvalues of positive-definite matrices,? Tr. Mat. Inst. Akad. Nauk SSSR,84, 5?7 (1965). · Zbl 0176.13602
[154] V. N. Kublanovskaya, ?On the computation of the generalized inverse matrix and projector,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 2, 326?332 (1966).
[155] V. N. Kublanovskaya, ?On a method of triangular factorization of the inverse matrix,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 3, 555?556 (1966). · Zbl 0184.37601
[156] V. N. Kublanovskaya, ?On a method of solving the full eigenvalue problem for a degenerate matrix,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 4, 611?620 (1966).
[157] V. N. Kublanovskaya, ?On an iterative process for determining eigenvalues of small modulus of a matrix and their corresponding eigenvectors,? Tr. Mat. Inst. Akad. Nauk SSSR,96, 93?104 (1968).
[158] V. N. Kublanovskaya, ?On an application of Newton’s method to the determination of the eigenvalues of a matrix,? Dokl. Akad. Nauk SSSR,188, No. 5, 1004?1005 (1969).
[159] V. N. Kublanovskaya, ?On the application of orthogonal transformations to the solution of the eigenvalue problem for ?-matrices,? in: Questions of Accuracy and Effective Computational Alogrithms, Proc. Symp., Vol. 1, Kiev (1969), pp. 47?59.
[160] V. N. Kublanovskaya, ?Application of orthogonal transformations to the numerical realization of linear algebraic perturbation problems,? Zh. Vychisl. Mat. Mat. Fiz.,10, No. 2, 429?433 (1970). · Zbl 0222.65042
[161] V. N. Kublanovskaya, ?On an approach to the solution of the inverse eigenvalue problem,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,18, 138?149 (1970). · Zbl 0254.65028
[162] V. N. Kublanovskaya, ?Application of a normalized process to the solution of the inverse eigenvalue problem for a matrix,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,23, 72?83 (1971). · Zbl 0284.65031
[163] V. N. Kublanovskaya, ?Application of a normalized process to the solution of linear algebraic systems,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 5, 1091?1098 (1972).
[164] V. N. Kublanovskaya, ?Newton’s method for determining the eigenvalues and eigenvectors of a matrix,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 6, 1371?1380 (1972).
[165] V. N. Kublanovskaya, ?A normalized scheme of the square-root method and its application to the solution of some problems in algebra,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,35, 56?66 (1973).
[166] V. N. Kublanovskaya, ?On the solution of a nonlinear eigenvalue problem for a matrix,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,35, 67?74 (1973).
[167] V. N. Kublanovskaya, ?Two-sided approximations in the algorithms LR and QR,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 15?22.
[168] V. N. Kublanovskaya, ?On solution of the additive problem for the eigenvalues of a matrix,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,48, 12?17 (1974). · Zbl 0348.65034
[169] V. N. Kublanovskaya, G. V. Savinov, and T. N. Smirnova, ?On the solution of problems with sparse matrices,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,35, 75?94 (1973).
[170] V. N. Kublanovskaya and V. B. Khazanov, ?On an inverse eigenvalue problem for a matrix,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,23, 84?93 (1971). · Zbl 0284.65032
[171] V. Yu. Kudrinskii and V. S. Ostapchuk, ?On an estimate of the total error of the solution of degenerate systems of linear algebraic equations,? in: Mathematical Methods in Specialized Computational Techniques, Proc. Seminar, No. 1, Kiev (1968), pp. 57?69.
[172] V. Yu. Kudrinskii and V. S. Ostapchuk, ?On the solution of degenerate and poorly conditioned systems of linear algebraic equations,? in: Mathematical Methods in Specialized Computational Techniques, Proc. Seminar, No. 2, Kiev (1969), pp. 59?67.
[173] V. Yu. Kudrinskii and V. S. Ostapchuk, ?Some algorithms for solving systems of linear algebraic equations with rectangular matrices,? Vychisl. Prikl. Mat., Mezhved. Nauch. Sb.,12, 78?86 (1970).
[174] Yu. A. Kuznetsov, ?On the theory of iterative processes,? Dokl. Akad. Nauk SSSR,184, No. 2, 274?277 (1969).
[175] Yu. A. Kuznetsov, ?Interative methods and minimization of a functional,? in: Computational Methods in Transport Theory [in Russian], Atomizdat (1969), pp. 96?109.
[176] Yu. A. Kuznetsov, ?On symmetrization of iterative processes,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1969), pp. 30?40.
[177] Yu. A. Kuznetsov, ?Iterative methods of solving linear systems with singular matrices,? in: Mathematical Provisions for the Computer [in Russian], Kiev (1972), pp. 221?227.
[178] Yu. A. Kuznetsov, ?Iterative methods of solving incompatible systems of linear equations,? Vychisl. Tsentr Sib. Otd. Akad. Nauk SSSR, Serminar ?Vychisl. Metody Prikl. Mat.,? No. 6, Preprint, Novosibirsk (1974).
[179] Yu. A. Kuznetsov and A. M. Matsokin, ?On an application of the method of bisections,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 34?41.
[180] F. Kuhnert, ?On some iterative methods of seeking the eigenvalues of self-adjoint operators,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 1, 143?145 (1964).
[181] F. Kuhnert, ?On the convergence of the method of false perturbations for computing eigenvalues,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 4, 752?763 (1967).
[182] L. M. Kutikov, ?On the structure of matrices inverse to the correlation matrices of vector random processes,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 4, 764?773 (1967).
[183] V. A. Kutin, ?On the convergence of the method of random search for solving systems of linear algebraic equations,? Uch. Zap. Perm. Univ., No. 271, 84?93 (1973).
[184] N. E. Larchenko, ?On criteria of the condition of matrices and the precision of solving systems of normal equations,? Tr. Mosk. Inst. Inzh. Zemleustroistva,22, 57?65 (1964).
[185] V. I. Lebedev, ?On the iterative KR method,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 6, 1250?1269 (1967).
[186] V. I. Lebedev, ?On iterative methods of solving operator equations with a spectrum lying on several segments,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1969), pp. 58?61.
[187] V. I. Lebedev, ?On iterative methods of solving operator equations with spectrum lying on several segments,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 6, 1247?1252 (1969).
[188] V. I. Lebedev, ?On iterative methods of two-sided approximations,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1972), pp. 59?68.
[189] V. I. Lebedev, ?On optimization in iterative methods,? in: Mathematical Provision for the Computer [in Russian], Kiev (1972), pp. 109?135.
[190] V. I. Lebedev, ?Determination of the largest eigenvalue and the eigenfunction corresponding to it by an iterative method with Chebyshev parameters,? Vychisl. Tsentr Sib. Otd. Akad. Nauk SSSR, Seminar ?Vychisl. Metody Prikl. Mat.,? No. 11, Preprint, Novosibirsk (1975).
[191] V. I. Lebedev and S. A. Finogenov, ?On the order of choosing iterative parameters in the Chebyshev cyclic iteration method,? Zh. Vychisl. Mat. Mat. Fiz.,11, No. 2, 425?438 (1971). · Zbl 0221.65099
[192] V. I. Lebedev and S. A. Finogenov, ?On an algorithm for choosing the parameters in Chebyshev cyclic methods,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1972), pp. 21?27.
[193] V. I. Lebedev and S. A. Finogenov, ?Solution of the problem of ordering parameters in Chebyshev iterative methods,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 1, 18?33 (1973). · Zbl 0249.65043
[194] V. I. Lebedev and S. A. Finogenov, ?On stability in Chebyshev iterative processes,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 42?47.
[195] A. A. Levin, ?On a method of solving the partial eigenvalue problem,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 4, 732?737 (1965).
[196] É. D. Levinson, ?On quadratic convergence of the Jacobi method in the case of multiple eigenvalues,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 3, 556?559 (1966).
[197] S. M. Lozinskii, ?An estimate of the error of numerical integration of ordinary differential equations. I,? Izv. Vyssh. Uchebn. Zaved., Mat.,5, 52?90 (1958).
[198] S. M. Lozinskii, ?On the theory of finite matrices,? Dokl. Akad. Nauk SSSR,163, No. 4, 809?811 (1965).
[199] S. M. Lozinskii, ?Estimates of the spherical matrix norm and the logarithmic norm corresponding to it,? Dokl. Akad. Nauk SSSR,165, No. 4, 763?766 (1965).
[200] S. M. Lozinskii, ?Norms of matrices and their applications to the estimate of eigenvalues of matrices and to differential equations,? Vestn. Leningr. Gos. Univ., No. 13, 51?61 (1968).
[201] Yu. I. Lyubich, ?On operator norms of matrices,? Usp. Mat. Nauk,18, No. 4, 161?164 (1963). · Zbl 0161.02902
[202] Yu. I. Lyubich, ?Condition in general computational problems,? Dokl. Akad. Nauk SSSR,171, No. 4, 791?793 (1966). · Zbl 0198.47902
[203] Yu. I. Lyubich, ?Rates of convergence of coordinate relaxation for a quadratic functional,? Dokl. Akad. Nauk SSSR,173, No. 1, 37?39 (1967). · Zbl 0183.17702
[204] G. Ya. Lyakhovetskii, ?On the escalator method of determining eigenvalues and eigenvectors of Hermitian matrices and on the successive introduction of vectors into a principal basis,? Zh. Vychisl. Mat. Mat. Fiz.,14, No. 6, 1378?1385 (1974).
[205] I. N. Lyashchenko, ?On a generalization of the escalator method of finding eigenvalues of matrices,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 3, 676?679 (1969).
[206] M. I. Mavlyanova, ?On the power process of determining eigenvalues and eigenvectors of polynomial matrices,? in: Questions of Computational and Applied Mathematics [in Russian], No. 39, Tashkent (1970), pp. 88?95. · Zbl 0263.65045
[207] M. I. Mavlyanova, ?Application of orthogonal transformations to the determination of the eigenvalues and eigenvectors of polynomial matrices,? in: Questions of Computational and Applied Mathematics [in Russian], No. 41, Tashkent (1970), pp. 68?73.
[208] M. I. Mavlyanova, ?Solution of the partial eigenvalue problem for a polynomial matrix,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,18, 116?124 (1970). · Zbl 0263.65045
[209] V. A. Magarik, ?On the matrices of Young,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 2, 195?202 (1966). · Zbl 0154.17001
[210] V. A. Magarik, ?On the relaxation factor for systems with Young matrices,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 5, 824?830 (1966). · Zbl 0154.17001
[211] V. A. Magarik, ?The symmetrized Seidel method for non-self-adjoint systems of linear algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 2, 404?405 (1967). · Zbl 0175.45901
[212] V. A. Magarik, ?Best and oscillatory symmetrized relaxation,? Zh. Vychisl. Mat.-Mat. Fiz.,9, No. 1, 182?185 (1969). · Zbl 0165.50302
[213] B. F. Magus’kin, ?The connection of the method of conjugate directions with triangular factorization,? Izv. Vyssh. Uchebn. Zaved., Geod. Aeorfotos’ldemka, No. 6, 65?75 (1962).
[214] G. D. Maistrovskii, ?Relaxation theory of Jacobi methods,? Dokl. Akad. Nauk SSSR,176, No. 5, 1004?1006 (1967). · Zbl 0272.65024
[215] N. G. Maksimovich, ?On a method of solving a system of algebraic equations in application to the calculation of electric circuits,? Proc. Seminar on Methods of Mathematical Modeling and the Theory of Electric Circuits, Inst. Kibern. Akad. Nauk Ukr. SSR,1, 191?200 (1963).
[216] A. I. Mal’tsev, Foundations of Linear Algebra [in Russian], 3rd ed., Nauka, Moscow (1970).
[217] B. O. Marder, ?Estimate of the error of the solution of systems of linear algebraic equations caused by errors in the initial data,? in: Automation of the Solution of Problems of Machine Dynamics [in Russian], Nauka, Moscow (1973), pp. 134?136.
[218] Yu. I. Markuze, ?On the question of estimating irremovable errors in solving linear systems,? Izv. Vyssh. Uchebn. Zaved., Geod. Aerofotos ?emka, No. 4, 34?38 (1969).
[219] G. I. Marchuk, ?On the theory of iterative processes,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1969), pp. 4?10.
[220] G. I. Marchuk, Methods of Numerical Mathematics, Springer-Verlag (1975). · Zbl 0329.65002
[221] G. I. Marchuk and Yu. A. Kuznetsov, ?On the question of optimal iterative processes,? Dokl. Akad. Nauk SSSR,181, No. 6, 1331?1334 (1968).
[222] G. I. Marchuk and Yu. A. Kuznetsov, ?Some questions of the theory of multistep iterative processes,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1969), pp. 16?29.
[223] G. I. Marchuk and Yu. A. Kuznetsov, ?On the solution of systems of linear equations by iterative methods,? in: Questions of Accuracy and Effective Computational Algorithms [in Russian], Proc. Symposium, Vol. 1, Kiev (1969), pp. 60?74.
[224] G. I. Marchuk and Yu. A. Kuznetsov, ?Some questions in iterative methods,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1972), pp. 4?20.
[225] G. I. Marchuk and Yu. A. Kuznetsov, Iterative Methods and Quadratic Functionals [in Russian], Nauka, Sib. Otd., Novosibirsk (1972).
[226] G. I. Marchuk and N. N. Yanenko, ?Application of the splitting method (fractional steps) for solving problems of mathematical physics,? in: Some Questions of Computational and Applied Mathematics [in Russian], Nauka, Novosibirsk (1966), pp. 5?22.
[227] A. A. Matveev, ?On an algorithm for the pseudoinversion of matrices,? Zh. Vychisl. Mat. Mat. Fiz.,14, No. 2, 483?487 (1974).
[228] I. N. Molchanov and L. D. Nikolenko, ?On a generalized solution of class of systems of linear algebraic equations with a degenerate matrix,? in: Numerical Analysis [in Russian], Proc. Seminar, No. 2, Kiev (1969), pp. 59?72.
[229] I. N. Molchanov and L. D. Nikolenko, ?On a direct method of solving Neumann problems for the Poisson equation,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 6, 1607?1612 (1973).
[230] I. N. Molchanov, L. D. Nikolenko, and M. P. Kirichenko, ?On a packet of programs for solving systems of linear algebraic equations,? Kibernetika, No. 1, 127?133 (1972). · Zbl 0233.65030
[231] I. N. Molchanov and M. F. Yakovlev, ?On rapidly convergent iterative processes for the solution of systems of difference equations with a nonunique solution,? in: Questions of Accuracy and Effective Computational Algorithms [in Russian], Proc. Symp., Vol. 1, Kiev (1969), pp. 75?87.
[232] I. N. Molchanov and M. F. Yakovlev, ?On a class of iterative processes for solving incompatible systems of linear algebraic equations,? Dokl. Akad. Nauk SSSR,209, No. 4, 782?784 (1973). · Zbl 0297.65031
[233] I. N. Molchanov and M. F. Yakovlev, ?On two-step iterative methods for solving a class of incompatible systems of linear algebraic equations,? Dokl. Akad. Nauk SSSR,214, No. 6, 1265?1268 (1974). · Zbl 0301.65019
[234] P. I. Monastyrnyi, ?A version of the method of rotations,? Dokl. Akad. Nauk BSSR,12, No. 7, 588?590 (1968).
[235] P. I. Monastyrnyi, ?On the decomposition of a matrix into a product of an orthogonal and right triangular matrix,? Dokl. Akad. Nauk BSSR,13, No. 5, 392?393 (1969).
[236] V. A. Morozov, ?On regularization of incorrectly posed problems and the choice of the regularization parameter,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 1, 170?175 (1966). · Zbl 0176.13103
[237] V. A. Morozov, ?On the error principle in solving operator equations by the method of regularization,? Zh. Vychisl. Mat. Mat. Fiz.,8, No. 2, 295?309 (1968).
[238] V. A. Morozov, ?On optimal approximate solutions of systems of linear algebraic equations,? in: Questions of Accuracy and Effective Computational Algorithms [in Russian], Proc. Symp., Vol. 1, Kiev (1969), pp. 88?95.
[239] V. A. Morozov, ?On pseudosolutions,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 6, 1387?1391 (1969).
[240] V. A. Morozov, ?On optimal regularization of operator equations,? Zh. Vychisl. Mat. Mat. Fiz.,10, No. 4, 818?829 (1970).
[241] V. A. Morozov, ?On an effective numerical algorithm for constructing pseudosolutions,? Zh. Vychisl. Mat. Mat. Fiz.,11, No. 1, 260?262 (1971).
[242] V. A. Morozov, ?The method of regularization and the solution of systems of linear algebraic equations,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1972), pp. 64?69.
[243] V. A. Morozov, ?On the computation of lower bounds of functionals on the basis of approximate information,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 4, 1045?1049 (1973).
[244] V. A. Morozov, ?On the error principle for the solution of incompatible systems by the method of regularization of A. N. Tikhonov,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 5, 1099?1111 (1973).
[245] V. A. Morozov, ?On stable methods of solving systems of linear algebraic equations,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 57?62.
[246] V. A. Morozov, ?Linear and nonlinear incorrect problems,? in: Mathematical Analysis [in Russian], (Itogi Nauki i Tekhn., VINITIAN SSSR), Moscow (1973), pp. 129?178.
[247] I. I. Moskvitina, ?On rounding errors in the solution of a system of linear equations by the method of orthogonalization,? Dokl. Nauch. Konf., Yaroslavsk. Gos. Pedagog. Inst.,1, No. 3, 104?108 (1962).
[248] Yu. V. Mokhov, ?Loss of accuracy in solving systems of normal equations,? Izv. Vyssh. Uchebn. Zaved., Geod. Aerofotos’emka, No. 1, 45?61 (1965).
[249] M. V. Murav’eva, ?On optimal and limiting properties of the Bayes solution of a system of linear algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,13, No. 4, 819?828 (1973).
[250] I. V. Nartya, ?Expansion of the determinant of a tridiagonal secular equation,? Tr. Kishinevsk. S.-kh. Inst.,55, 85?90 (1968).
[251] E. S. Nikolaev, ?On the optimization of a two-step iterative method,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 6, 1456?1464 (1972).
[252] E. S. Nikolaev and A. A. Samarskii, ?A Richardson method stable for any number of iterations,? Inst. Prikl. Mat. Akad. Nauk SSSR, Preprint, No. 23, Moscow (1972).
[253] E. S. Nikolaev and A. A. Samarskii, ?Methods for the numerical solution of the Dirichlet problem for the Poisson equation in any dimension,? Dokl. Akad. Nauk SSSR,206, No. 4, 815?818 (1972). · Zbl 0266.65069
[254] E. S. Nikolaev and A. A. Samarskii, ldThe choice of iterative parameters in the Richardson method,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 4, 960?973 (1972).
[255] E. S. Nikolaev and A. A. Samarskii, ?On computational stability of two-layer and three-layer iterative schemes,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 5, 1197?1207 (1972).
[256] L. D. Nikolenko, ?Solution of a perturbed system of linear algebraic equations when the unperturbed equation is degenerate,? Ukr. Mat. Zh.,19, No. 4, 132?138 (1967). · doi:10.1007/BF01090411
[257] L. D. Nikolenko, ?On the construction of approximations to eigenvalues and eigenvectors of the ?perturbed? matrix,? in: Basic and Standard Programs for Computers and Systems [in Russian], Proc. Seminar, No. 1, Kiev (1968), pp. 33?43.
[258] L. D. Nikolenko, ?On an approach to the analysis and solution of a system of linear algebraic equations on a computer with variable digitation,? in: Basic and Standard Programs for Computing Machines and Systems [In Russian], Tr. Seminar, No. 2, Kiev, 1968 (1969), pp. 87?96.
[259] L. D. Nikolenko, ?On an estimate of accuracy of the solution of a system of linear algebraic equations,? in: Questions of Accuracy and Effective Computational Algorithms [in Russian], Proc. Symp., Vol. 1, Kiev (1969), pp. 96?108.
[260] V. S. Ostapchuk, ?On a method of solving degenerate algebraic systems,? Visn. Kiiv. Univ., Ser. Mat. Mekh., No. 16, 95?100 (1974).
[261] A. Yu. Ostrovskii, ?Algorithms for finding the positive-definite square root of a symmetric matrix,? Tr. Ts NII Stroit. Konstruktsii,9, 22?28 (1970).
[262] A. Yu. Ostrovskii, ?Finding ?max in the generalized eigenvalue problem for symmetric positive-definite matrices,? Tr. Ts NII Stroit. Konstruktsii,9, 50?54 (1970).
[263] V. Ya. Pan, ?On schemes of computing the product of matrices and the inverse matrix,? Usp. Mat. Nauk,27, No. 5, 249?250 (1972).
[264] V. V. Penenko and G. S. Rivin, ?The full eigenvalue problem for a Jacobi matrix,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1969), pp. 62?68.
[265] M. Petkov, ?A generalized reflection matrix,? Izv. Mat. Inst. B?lg.Akad. Nauk,11, 257?260 (1970). · Zbl 0223.15016
[266] M. Petkov, ?On a method of inverting matrices and solving linear systems,? Izv. Mat. Inst. B?lg. Akad. Nauk,13, 131?139 (1972).
[267] M. Petkov, ?On a method of elimination,? Izv. Mat. Inst. B?lg. Akad. Nauk,14, 29?34 (1973).
[268] N. V. Petri and Kh. D. Ikramov, ?On extremal properties of some matrix norms,? Zh. Vychisl. Mat. Mat. Fiz.,8, No. 4, 865?871 (1968).
[269] R. V. Petrina, ?The square-root method in the packet of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 9, Moscow State Univ. (1974), pp. 20?36.
[270] A. Ya. Povzner, ?On a method of computing the eigenvalues of matrices,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 5, 903?907 (1965).
[271] A. F. Potapova, ?On acceleration of convergence of the method of fastest descent,? Zh. Vychisl. Mat. Mat. Fiz.,11, No. 3, 749?752 (1971).
[272] G. P. Prokopov, ?On a method of finding the maximal eigenvalue of a symmetric matrix,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 5, 1167?1171 (1967).
[273] B. P. Pugachev, ?Approximate computation of eigenvectors,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 2, 340?343 (1964).
[274] B. P. Pugachev, ?On the application of the trace of a matrix to the computation of its eigenvalues,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 1, 114?116 (1965).
[275] B. P. Pugachev, ?On the approximate computation of eigenvalues and eigenvectors,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 4, 729?732 (1965).
[276] B. P. Pugachev, ?Use of poorly convergent iterative processes for the solution of systems of linear equations,? Zh. Vychisl. Mat. Mat. Fiz.,8, No. 6, 1318?1321 (1968).
[277] B. P. Pugachev, ?Computation of the eigenvalues of largest modulus of a matrix by an iterative method,? in: Application of Methods of Computational Mathematics and Computing Techniques to the Solution of Scientific-Research and Economics Problems [in Russian], No. 4, Voronezh (1969), pp. 93?95.
[278] B. P. Pugachev, ?On the application of divergent iterative processes in the solution of linear equations,? Tr. Mat. Fak. Voronezh. Univ.,3, 22?26 (1972).
[279] E. Ya. Remez, Foundations of Numerical Methods of Chebyshev Approximation [in Russian], Naukova Dumka, Kiev (1969).
[280] M. Ya. Rozanov, ?Homogeneous computational structures and numerical methods for the solution of problems of linear algebra,? Nauch. Tr. Mosk. Inzh. Ekon. Inst.,63, 53?86 (1973).
[281] A. A. Samarskii, ?On an economical algorithm for the numerical solution of systems of differential and algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 3, 580?585 (1964).
[282] A. A. Samarskii, ?Some questions in the theory of difference schemes,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 4, 665?686 (1966).
[283] A. A. Samarskii, ?On a choice of iteration parameters in the method of variable directions for the difference Dirichlet problem of higher order of accuracy,? Dokl. Akad. Nauk SSSR,179, No. 3, 548?551 (1968).
[284] A. A. Samarskii, ?Two-layer iteration schemes,? Dokl. Akad. Nauk SSSR,185, No. 3, 524?527 (1969).
[285] A. A. Samarskii, ?Iterative two-layer schemes for non-self-adjoint equations,? Dokl. Akad. Nauk SSSR,186, No. 1, 35?38 (1969).
[286] A. A. Samarskii, ?Some questions of the general theory of difference schemes,? in: Partial Differential Equations [in Russian], Nauka, Moscow (1970), pp. 191?223.
[287] A. A. Samarskii, Introduction to the Theory of Difference Schemes [in Russian], Nauka, Moscow (1971).
[288] A. A. Samarskii and V. B. Andreev, ?Iterative schemes of variable directions for the numerical solution of the Dirichlet problem,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 6, 1025?1036 (1964).
[289] B. A. Samokish, ?Gradient relaxation in the Jacobi method,? in: Computational Methods [in Russian], No. 2, Leningrad Univ. (1963), pp. 3?9.
[290] V. K. Saul’ev, ?On the computation of eigenvectors of matrices by the method of double iterations,? Zh. Vychisl. Mat. Mat. Fiz.,3, No. 6, 1112?1113 (1963).
[291] M. P. Simoyu, ?An iterative method of inverting matrices,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 4, 726?728 (1965).
[292] A. A. Skripii and V. S. Ostapchuk, ?On the solution of systems of normal equations and an estimate of total error,? in: Questions of Accuracy and Effective Computational Algorithms [in Russian], Proc. Symp., Vol. 1, Kiev (1969), pp. 109?121.
[293] E. I. Sologub and L. P. Shchupov, ?Solution of systems of linear algebraic equations with a large number of zero elements on the computer,? Sb. Nauch. Tr. N.-I. i Proektn. Inst. po Obogashch. i Aglomer. Rud. Chern. Met.,12, 46?53 (1971).
[294] P. M. Sosis, ?On methods of solving systems of linear equations with sparse coefficient matrices on computers,? in: Investigations in the Theory of Construction [in Russian], No. 12, Gosstroiizdat, Moscow (1963), pp. 281?287.
[295] V. Ya. Stetsenko, ?On a method of accelerating convergence of iterative processes,? Dokl. Akad. Nauk SSSR,178, No. 5, 1021?1024 (1968).
[296] M. Stoyakovich, ?Inversion of matrices that arise in the application of the method of least squares,? Zh. Vychisl. Mat. Mat. Fiz.,4, No. 5, 911?915 (1964).
[297] U. M. Sultangazin, ?On a method of solving systems of linear algebraic equations,? Sb. Tr. Soiskatelei i Aspirantov, M-vo Vyssh. i Sredn. Spets. Obrazovaniya KazSSR,1, No. 1, 96?103 (1963).
[298] U. M. Sultangazin, ?On a gradient method of finding the eigenvector belonging to the least eigenvalue of a positive-definite matrix,? Proc. 1st Kazakhstan Interschool Scientific Conference on Mathematics and Mechanics, 1963, Nauk, Alma-Ata (1965), pp. 182?184.
[299] U. M. Sultangazin, ?On the question of solving a linear system of equations with many right sides by the bordering method,? in: Mat. Mekh., No. 3, Alma-Ata (1968), pp. 142?148.
[300] U. M. Sultangazin and N. Sakhanov, ?On the question of solving poorly conditioned systems of linear algebraic equations,? Proc. 3rd Kazakhstan Interschool Scientific Conference on Mathematics and Mechanics [in Russian], 1967, Nauka, Alma-Ata (1970), pp. 173?174.
[301] R. Tavast, ?On the factorization of block matrices,? Izv. Akad. Nauk EstSSR, Fiz. Mat.,21, No. 3, 313?316 (1972).
[302] A. N. Tikhonov, ?On incorrect problems of linear algebra and a stable method for their solution,? Dokl. Akad. Nauk SSSR,163, No. 3, 591?594 (1965). · Zbl 0196.48001
[303] A. N. Tikhonov, ?On the stability of algorithms for the solution of degenerate systems of linear algebraic equations,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 4, 718?722 (1965).
[304] A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Incorrect Problems [in Russian], Nauka, Moscow (1974).
[305] A. F. Turbin, ?Formulas for computing semiinverse and pseudoinverse matrices,? Zh. Vychisl. Mat. Mat. Fiz.,14, No. 3, 772?775 (1974).
[306] D. K. Faddeev, ?On norms in spaces of polylinear forms,? Zh. Vychisl. Mat. Mat. Fiz.,12, No. 2, 521?525 (1972).
[307] D. K. Faddeev, ?On an algebra of matrices and its applications to computational problems,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 11?14.
[308] D. K. Faddeev, V. N. Kublanovskaya, and V. N. Faddeeva, ?Linear algebraic systems with rectangular matrices,? in: Modern Numerical Methods [in Russian], No. 1 (Materials of the International Summer School on Numerical Methods, Kiev, 1966), Moscow (1968), pp. 16?75. · Zbl 0208.40001
[309] D. K. Faddeev, V. N. Kublanovskaya, and V. N. Faddeeva, ?On the solution of linear algebraic systems with rectangular matrices,? Tr. Mat. Inst. Akad. Nauk SSSR,96, 76?92 (1968). · Zbl 0208.40001
[310] D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra [in Russian], 2nd ed., Fizmatgiz, Moscow-Leningrad (1963). · Zbl 0112.07503
[311] D. K. Faddeev and V. N. Faddeeva, ?The problem of scaling for linear systems,? in: Modern Numerical Methods [in Russian], No. 1 (Materials of the International Summer School on Numerical Methods, Kiev, 1966), Moscow (1968), pp. 76?84.
[312] D. K. Faddeev and V. N. Faddeeva, ?On natural norms for estimating solutions of a finite computational problem,? Zh. Vychisl. Mat. Mat. Fiz.,9, No. 1, 3?13 (1969).
[313] D. K. Faddeev and V. N. Faddeeva, ?Natural norms in algebraic processes,? in: Questions of Accuracy and Effective Computational Algorithms [in Russian], Proc. Symp., Vol. 1, Kiev (1969), pp. 122?141.
[314] D. K. Faddeev and V. N. Faddeeva, ?The accompanying matrix and estimation of the solution of a finite computational problem,? in: Computational Methods of Linear Algebra, Novosibirsk (1973), pp. 4?10.
[315] D. K. Faddeev and V. N. Faddeeva, ?On the question of solving linear algebraic systems,? Zh. Vychisl. Mat. Mat. Fiz.,14, No. 3, 539?558 (1974). · Zbl 0285.65024
[316] V. N. Faddeeva, ?Triangular-orthogonal methods for solving the full eigenvalue problem,? Zh. Vychisl. Mat. Mat. Fiz.,3, No. 3, 559?560 (1963).
[317] V. N. Faddeeva, ?A shift for systems with poorly conditioned matrices,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 5, 907?911 (1965).
[318] V. N. Faddeeva, ?On some extremal problems for matrix norms,? Zh. Vychisl. Mat. Mat. Fiz.,7, No. 2, 401?404 (1967). · Zbl 0186.05902
[319] S. Falk, ?Stabilization of poorly conditioned systems of linear algebraic equations by means of the Jacobi method,? Zh. Vychisl. Mat. Mat. Fiz.,3, No. 2, 358?361 (1963).
[320] Fam Van At, ?Reduction of a positive-definite matrix to a quasistochastic matrix by the method of similarity transformation,? Zh. Vychisl. Mat. Mat. Fiz.,11, No. 6, 1563?1567 (1971). · Zbl 0256.65026
[321] R. P. Fedorenko, ?Iterative methods for solving difference elliptic equations,? Usp. Mat. Nauk,28, No. 2, 121?182 (1973). · Zbl 0278.65105
[322] M. Fiedler and V. Prak, ?Estimates and iterative methods for finding a simple eigenvalue of an almost decomposable matrix,? Dokl. Akad. Nauk SSSR,151, No. 4, 790?792 (1963).
[323] E. I. Filippovich, ?On solution of poorly conditioned systems of linear algebraic equations,? Vychisl. Mat., Mezhved. Nauch. Sb.,2, 78?88 (1966).
[324] V. T. Frolkin, V. N. Il’in, and V. L. Kogan, ?An effective method of solving sparse systems of linear equations of high order,? Izv. Vyssh. Ucheb. Zaved., Radioelektron.,17, No. 8, 15?23 (1974).
[325] V. B. Khazanov, ?A remark on the Danilevsky method,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,35, 142?145 (1973).
[326] V. Khmurna, ?Solution of systems of linear equations with n-diagonal matrices,? Apl. Mat.,10, No. 3, 222?225 (1965).
[327] Sh. Khodzhiev, ?On the generalized solution of arbitrary systems of linear equations,? Dokl. Akad. Nauk TadzhSSR,14, No. 7, 7?8 (1971). · Zbl 0706.15002
[328] N. N. Kholmogorov, ?On the solution of three-term systems of linear algebraic equations of general form,? in: Questions of Calculation in Modern Metal and Wood Construction [in Russian], Rostov-on-Don (1973), pp. 118?120.
[329] N. N. Kholmogorov, ?On the solution of arbitrary systems of systems of linear algebraic equations by the method of separation of variables,? in: Questions of Calculation in Modern Metal and Wood Construction [in Russian], Rostov-on-Don (1973), pp. 121?122.
[330] Kho Tkhuan, ?On a method of inverting block tridiagonal matrices,? Zh. Vychisl. Mat. Mat. Fiz.,11, No. 6, 1557?1562 (1971).
[331] S. L. Khublarova, ?An algorithm for solving large systems of normal equations by the multigroup method on a computer,? Tr. Tsentr. N.-I. Inst. Geod., Aeros?emki Kartogr.,147, 17?33 (1962).
[332] I. V. Chepurina, ?Solution of systems with a Teoplitz matrix in the packet of linear algebra,? in: Numerical Analysis in FORTRAN [in Russian], No. 3, Moscow State Univ. (1973), pp. 152?162.
[333] I. V. Chepurina, ?Some modifications of the macromodule for computing the scalar product of vectors (SCO6A),? in: Numerical Analysis in FORTRAN [in Russian], No. 9, Moscow State Univ. (1974), pp. 137?147.
[334] A. V. Chernyi, ?On the numerical solution of systems of linear equations with poorly conditioned matrices which arise in practical problems of interpreting gravitational and magnetic anomalies,? in: Application of Some Mathematical Methods to the Interpretation of Geophysical Data [in Russian], Nauka, Novosibirsk (1967), pp. 114?132.
[335] V. V. Shaidurov, ?Extension with respect to a parameter in the method of regularization,? in: Computational Methods of Linear Algebra [in Russian], Novosibirsk (1973), pp. 77?85.
[336] V. E. Shamanskii and L. V. Éllanskaya, ?The general scheme of methods of block iteration,? Vychisl. Mat., Mezhved, Nauch. Sb.,1, 41?52 (1965).
[337] S. G. Sharupich, ?On a block solution of systems of linear equations,? Izv. Vyssh. Uchebn. Zaved., Geod. Aerofotos?emka, No. 1, 28?33 (1969).
[338] V. S. Shishov, ?On stationary pairs of points of the iterative process for determining eigenvalues,? Zh. Vychisl. Mat. Mat. Fiz.,6, No. 2, 332?335 (1966).
[339] S. M. Shugrin, ?On the correctness of the method of elimination for solving algebraic systems of equations,? in: Dynamics of Continuous Media [in Russian], No. 5, Novosibirsk (1970), pp. 96?117.
[340] S. M. Shugrin, ?On an iterative method,? Sib. Mat. Zh.,12, No. 3, 684?689 (1971). · Zbl 0228.65046 · doi:10.1007/BF00969726
[341] S. I. Shudrova, ?Application of the two-parameter method of fastest descent to the solution of a system of linear algebraic equations,? Uch. Zap. Leningr. Gos. Univ.,68, 165?178 (1969).
[342] A. I. Erlikh and V. L. Ven, ?On numerical solution of matrix equations of the form WX=Y which are compatible for any right side,? Zh. Vychisl. Mat. Mat. Fiz.,10, No. 4, 1027?1029 (1970). · Zbl 0212.17003
[343] M. F. Yakovlev, ?On some numerical methods of solving systems of difference equations with nonsymmetric and degenerate matrices,? in: Basic and Standard Programs for Computing Machines and Systems [in Russian], Proc. Seminar, No. 2, Kiev, 1968 (1969), pp. 104?110.
[344] M. F. Yakovlev, ?Application of explicit iterative methods for finding generalized solutions of incomtible systems of difference equations with a symmetric and nonnegative matrix,? in: Numerical Analysis [in Russian], Proc. Seminar, No. 2, Kiev (1969), pp. 123?134.
[345] N. N. Yanenko, ?Some questions in the theory of convergence of difference schemes with constant and variable coefficients,? Proc. 4th All-Union Mathematics Congress [in Russian], 1961, Vol. 2, Nauka, Leningrad (1964), pp. 613?621.
[346] N. N. Yanenko, The Method of Fractional Steps of Solving Multidimensional Problems of Mathematical Physics [in Russian], Nauka, Siberian Branch, Novosibirsk (1967). · Zbl 0183.18201
[347] J. O. Aasen, ?On the reduction of a symmetric matrix to tridiagonal form,? BIT,11, No. 3, 233?242 (1971). · Zbl 0242.65032 · doi:10.1007/BF01931804
[348] J. O. Aasen and W. Romberg, ?Eine Lösungsmethode für Eigenwertprobleme,? BIT,5, No. 4, 221?229 (1965). · Zbl 0154.40402 · doi:10.1007/BF01937501
[349] N. N. Abdelmalek, ?Round off error analysis for Gran-Schmidt method and solution of linear leastsquares problems,? BIT,11, No. 4, 345?367 (1971). · Zbl 0236.65031 · doi:10.1007/BF01939404
[350] A. A. Abramov, ?Calculation of matrix eigenvectors and eigenvalues, arising in the approximate solution of equations of mathematical physics,? Proc. IFIP Congr. 62, Munich, 9162, Amsterdam, North-Holland (1963).
[351] H. Akaike, ?Block Toeplitz matrix inversion,? SIAM J. Appl. Math.,24, No. 2, 234?241 (1973). · Zbl 0251.65024 · doi:10.1137/0124024
[352] F. A. Akyuz and S. Utku, ?An automatic node-relabeling scheme for bandwidth minimization of stiffness matrices,? AlAA J.,6, No. 4, 728?730 (1968).
[353] E. L. Albasiny, ?Error in digital solution of linear problems,? in: Error in Digital Computation, Vol.1, Wiley, New York-Sydney (1965), pp. 131?184.
[354] H.-J. Albrand, ?Über ein modifiziertes Gesamtschrittverfahren,? Beitr. Numerisch. Math. 2, Berlin, 7?11 (1974). · Zbl 0296.65014
[355] J. Albrecht, ?Fehlerschranken und Konvergenzbeschleunigung bei monotonen oder alternierenden Iterationsfolgen,? Z. Angew. Math. Mech.,42, Sonderh., T4-T6 (1962). · Zbl 0114.31902
[356] J. Albrecht, ?Fehlerschranken und Konvergenzbeschleunigung bei einer monotonen oder alternierenden Iterations folge,? Numer. Math.,4, No. 3, 196?208 (1962). · Zbl 0107.33301 · doi:10.1007/BF01386313
[357] J. Albrecht, ?Iterationsverfahren bester Strategie zur Lösung linearer Gleichungssysteme mit positiv definiter Koeffizientenmatrix,? Z. Angew. Math. Mech.,43, Sondern., T4-T8 (1963). · Zbl 0134.13206 · doi:10.1002/zamm.19630431303
[358] J. Albrecht, ?Zur Fehlerabschätzungbeim Gesamt- und Einzelschrittverfahren für lineare Gleichungs-systeme,? Z. Angew. Math. Mech.,43, Nos. 1?2, 83?85 (1963). · Zbl 0112.07604 · doi:10.1002/zamm.19630430110
[359] G. Alefeld, ?Intervallrechnung über den komplexen Zahlen und einige Anwendungen,? Diss. Univ. Karlsruhe (1968).
[360] G. Alefeld, ?Über die asymptotische Konvergenzgeschwindigkeit des allgemeinen Relaxat ions ver fahrens bei nichtnegativen Matrizen,? Computing,3, No. 4, 258?267 (1968). · Zbl 0181.17203 · doi:10.1007/BF02235392
[361] G. Alefeld, ?Bemerkungen zur Einschliessung der Lösung eines linearen Gleichungssystemes,? Z. Angew. Math. Mech.,50, Sonderh. 1?4, T33-T35 (1970).
[362] G. Alefeld, ?Über die aus monoton zerlegbaren Operatoren gebildeten Iterationsverfahren,? Computing,6, Nos. 1?2, 161?172 (1970). · Zbl 0211.46603 · doi:10.1007/BF02241742
[363] G. Alefeld, ?Anwendungen des Fixpunktsatzes für Pseudometrische Räume in der Intervallrechnung,? Numer. Math.,17, No. 1, 33?39 (1971). · Zbl 0222.65041 · doi:10.1007/BF01395863
[364] G. Alefeld, ?Verallgemeinerung des Schulzschen Iterations Verfahrens,? Z. Angew. Math. Mech.,J51, Sonderh., T33. (1971). · Zbl 0222.65052 · doi:10.1002/zamm.19710510902
[365] G. Alefeld, ?Über konvergente Zerlegungen von Matrizen,? Numer. Math.,20, No. 4, 312?316 (1973). · Zbl 0248.65021 · doi:10.1007/BF01407373
[366] G. Alefeld and N. Apostolatos, ?Praktische Anwendung von Abschätzungsformeln bei Iterationsverfahren,? Z. Angew. Math. Mech.,48, No. 8, 46?49 (1968). · Zbl 0187.09903
[367] G. Alefeld and J. Herzberger, ?ALGOL-60 Algorithmen zur Auflösung lineare Gleichungssysteme mit Fehlererfassung,? Computing,6, Nos. 1?2, 28?34 (1970). · Zbl 0212.17002 · doi:10.1007/BF02241730
[368] G. Alefeld and J. Herzberger, ?Über die Berechnung der inversen Matrix mit Hilfe der Intervallrechnung,? Elektron. Rechenanlag,12, No. 5, 259?261 (1970). · Zbl 0208.40003
[369] G. Alefeld and J. Herzberger, ?Matrizeninvertierung mit Fehlererfassung,? Elektron. Datenverarb.,12, No. 9, 410?416 (1970). · Zbl 0199.49702
[370] G. Alefeld and J. Herzberger, ?Verfahren höherer Ordnung zur iterativen Einschliessung der inversen Matrix,? Z. Angew. Math. Phys.,21, No. 5, 819?824 (1970). · Zbl 0208.40101 · doi:10.1007/BF01594838
[371] G. Alefeld and J. Herzberger, ?Über die Verbesserung von Schranken für die Lösung bei linearen Gleichungssystemen,? Angew. Inf.,13, No. 3, 107?112 (1971). · Zbl 0213.16304
[372] G. Alefeld, J. Herzberger, and O. Mayer, ?Über neuere Gesichtspunkte beim numerischen Rechnen,? Math. Naturwiss. Unterr.,24, No. 8, 458?467 (1971). · Zbl 0243.65019
[373] Oliveira F. Aleixo, ?Inversion of strongly diagonally dominant matrices with control of errors,? Rev. Fac. Cienc. Univ. Lisboa,A13, No. 2, 251?257 (1970?1971).
[374] Oliveira F. Aleixo, ?Limitacão automática de erros na approximacão da solucao de equacoes,? Actas prim. Jorn. Mat. Lusoesp. Publs. Inst. ?Jorge Juan? Mat. Madrid, 327?340 (1973).
[375] G. G. Alway and D. W. Martin, ?An algorithm for reducing the bandwidth of a matrix of symmetrical configurations,? Comput. J.,8, No. 3, 264?272 (1965). · Zbl 0147.13103 · doi:10.1093/comjnl/8.3.264
[376] A. R. Amir-Moez and T. G. Newman, ?Geometry of generalized inverses,? Mat. Mag.,43, No. 1, 33?36 (1970). · Zbl 0192.36602 · doi:10.2307/2688109
[377] P. Anderson and G. Loizou, ?On the quadratic convergence of an algorithm which diagonalizes a complex symmetric matrix,? J. Inst. Math. Appl.,12, No. 3, 261?271 (1973). · Zbl 0273.65025 · doi:10.1093/imamat/12.3.261
[378] P. M. Anselone and L. B. Rall, ?The solution of characteristic value-vector problems by Newton’s method,? Numer. Math.,11, No. 1, 38?45 (1968). · Zbl 0162.46602 · doi:10.1007/BF02165469
[379] S. Aoustin, ?Etude de méthodes numériques directes pour la résolution de systèmes d’équations linéaires sur I. B. M. 650 standard,? Thèse Ingr-Doct. Fac. Sci. Univ. Nantes (1963).
[380] N. Apostolatos and U. Kulisch, ?Über die Konvergenz des Relaxationsverfahrens bei nicht-negativen und diagonaldominanten Matrizen,? Computing,2, No. 1, 17?24 (1967). · Zbl 0183.17803 · doi:10.1007/BF02235509
[381] N. Apostolatos and U. Kulisch, ?Grundlagen einer Maschinenintervallarithmetik,? Computing,2, No. 2, 89?104 (1967). · Zbl 0159.21203 · doi:10.1007/BF02239180
[382] N. Apostolatos and U. Kulisch, ?Grundzüge einer Interfallrechnung für Matrizen und einige Anwendungen,? Elektron. Rechenanlag.,10, No. 2, 73?83 (1968).
[383] N. Apostolatos, U. Kulisch, R. Krawczyk, B. Lortz, K. Nickel, and H. W. Wippermann, ?The algorithmic language Triplex-Algol 60,? Numer. Math.,11, No. 2, 175?180 (1968). · Zbl 0155.48702 · doi:10.1007/BF02165313
[384] I. Arany, L. Szoda, and W. F. Smith, ?An improved method for reduing the bandwidth of sparse symmetric matrices,? Proc. IFIP Congr. 71, Ljubljana, 1971, Amsterdam-London, North-Holland (1972).
[385] E. Arghiriade, ?Sur les matrices qui sont permutables avec leur inverse generalisee,? Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. e Natur.,35, No. 5, 244?251 (1963). · Zbl 0122.01703
[386] E. Arghiriade, ?Asupra inversei generalizate a unui produs de matrici,? An. Univ. Timisoara. Ser. Sti. Mat.-Fiz.,5, 37?42 (1967).
[387] E. Arghiriade, ?Remarques sur l’inverse generalisee d’un produit de matrices,? Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. e Natur.,42, No. 5, 621?625 (1967). · Zbl 0153.04802
[388] E. Arghiriade and G. Dragomir, ?Une nouvelle definition de l’inverse generalisee d’une matrice,? Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. e Natur.,35, Nos. 3?4, 158?165 (1963). · Zbl 0127.24703
[389] D. B. Arnurius, ?An algorithm for a form of the problem av equals lambda bv,? Oak Ridge National Laboratory Ornl. 3980 UC-32, Math, and Comput. (1966).
[390] R. L. Ashenhurst, ?Techniques for automatic error monitoring and control,? in: Error in Digital Computation, Vol. I, Wiley, New York-London-Sydney (1965), pp. 43?59.
[391] R. L. Ashenhurst, ?Experimental investigation of unnormalized arithmetic,? in: Error in Digital Computation, Vol. 2, Wiley, New York-London-Sydney (1965), pp. 3?37.
[392] R. L. Ashenhurst and N. C. Metropolis, ?Unnormalized floating point arithmetic,? J. Assoc. Comput. Mach.,6, No. 3, 415?428 (1959). · Zbl 0121.12102 · doi:10.1145/320986.320996
[393] R. L. Ashenhurst and N. C. Metropolis, ?Error estimation in computer calculation,? Amer. Math. Mon.,72, No. 2, Part II, 47?58 (1965). · Zbl 0216.49602 · doi:10.2307/2313310
[394] V. Ashkenazi, ?Geodetic normal equations,? in: Large Sparse Sets of Linear Equations, Academic Press, London-New York (1971), pp. 57?74.
[395] O. Axelsson, Generalized SSOR Methods, DD/7218, Geneva (1972).
[396] O. Axelsson, ?A generalized SSOR method,? BIT,12, No. 4, 443?467 (1972). · Zbl 0256.65046 · doi:10.1007/BF01932955
[397] G. Azumaya, ?Strongly ?-regular rings,? J. Fac. Sci., Hokkaido Univ.,13, No. 1, 34?39 (1954). · Zbl 0058.02503
[398] I. Babuska, ?Numerical stability in problems of linear algebra,? SIAM J. Numer. Anal.,9, No. 1, 53?77 (1972). · Zbl 0248.65026 · doi:10.1137/0709008
[399] P.-L. Baetsle, ?Calcul numerique des systemes algebriques lineaires de rang quelconque,? Coll. Calc. Num. et Math. Appl., Lille, 1964, 39?56, Paris (1967).
[400] Cl. Bahloul, ?Travaux de Marcuk? (Semin. Lions. Anal. Numer.), Fac. Sci.1, 5/01?5/13 (1969).
[401] D. E. Bailey, ?The effect on the solution of a problem of perturbations to the data. A study in interval arithmetic,? Math. Gaz.,57, No. 399, 26?36 (1973). · doi:10.1017/S0025557200131602
[402] M. D. Bakes, ?An alternative method of solution of certain tri-diagonal systems of linear equations,? Comput. J.,7, No. 2, 135?136 (1964). · Zbl 0229.65031 · doi:10.1093/comjnl/7.2.135
[403] E. H. Bareiss, ?Sylvester’s identity and multistep integer-preserving Gaussian elimination,? Math. Comput.,22, No. 103, 565?578 (1968). · Zbl 0187.09701
[404] G. P. Barker, ?Monotone norms,? Numer. Math.,18, No. 4, 321?326 (1972). · Zbl 0229.15013 · doi:10.1007/BF01404682
[405] G. P. Barker, ?Matricial norms over cones,? Linear Algebra Appl.,6, 175?182 (1973). · Zbl 0251.15024 · doi:10.1016/0024-3795(73)90017-7
[406] C. A. Barlow and E. L. Jones, ?A method for the solution of roots of a nonlinear equation and for solution of the general eigenvalue problem,? J. Assoc. Comput. Mach.,13, No. 1, 135?142 (1966). · Zbl 0149.11201 · doi:10.1145/321312.321323
[407] G. Barre, ?Sur la determination du facteur d’acceleration de convergence ? dans la resolution des systemes lineaires par la methode iterative des deplacements successifs,? C. R. Acad. Sci.,265, No. 16, A467-A469 (1967). · Zbl 0183.17901
[408] G. Barre, ?Sur la determination d’une valeur approchee du facteur d’acceleration de convergence optimal ?opt, dans la resolution des systemes lineaires par la methode iterative des deplacements successifs,? C. R. Acad. Sci.,266, No. 4, A230-A233 (1968). · Zbl 0176.13502
[409] R. H. Bartels and G. H. Golub, ?Stable numerical methods for obtaining the Chebyshev solution to an overdetermined system of equations,? Commun. ACM,11, No. 6, 401?406 (1968). · Zbl 0162.20701 · doi:10.1145/363347.363364
[410] W. Barth, R. S. Martin, and J. H. Wilkinson, ?Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection,? Numer. Math.,9, No. 5, 386?393 (1967). · Zbl 0189.47803 · doi:10.1007/BF02162154
[411] W. Barth and E. Nuding, ?Optimale Lösung von Intervallgleichungssystemen,? Computing,12, No. 2, 117?125 (1974). · Zbl 0275.65008 · doi:10.1007/BF02260368
[412] Giuseppe Basile, ?Some remarks on the pseudoinverse of a nonsquare matrix,? Atti Accad. Sci. Ist. Bologna. Cl. Sci. Fis. Rend.,6, Nos. 1?2, 236?240 (1968?1969).
[413] C. J. Bates, ?A computational technique for the effective handling of large matrices,? Int. J. Numer. Meth. Eng.,7, No. 1, 85?93 (1973). · doi:10.1002/nme.1620070107
[414] F. L. Bauer, ?On the definition of condition numbers and on their relation to closed methods for solving linear systems,? Proc. Int. Conf. Inform. Process., Unesco, Paris, 109?110 (1960).
[415] F. L. Bauer, ?Influence du choix du pivot sur l’erreur l’arrondi,? I-er Congr. Assoc. Franc. Calcul. Grenoble, 1960, Paris (1961), pp. 145?150.
[416] F. L. Bauer, ?On the field of values subordinate to a norm,? Numer. Math.,4, No. 2, 103?113 (1962). · Zbl 0117.11004 · doi:10.1007/BF01386300
[417] F. L. Bauer, ?Optimally scaled matrices,? Numer. Math.,5, No. 1, 73?87 (1963). · Zbl 0107.10501 · doi:10.1007/BF01385880
[418] F. L. Bauer, ?Optimal scaling of matrices and the importance of the minimal condition,? Proc. IFIP Congr. 62, Munich, 1962, Amsterdam, North-Holland (1963), pp. 198?200.
[419] F. L. Bauer, ?Numerische Abschätzung und Berechnung von eigenweten nichtsymmetrischer Matrizen,? Apl. Mat.,10, No. 2, 178?189 (1965). · Zbl 0156.16302
[420] F. L. Bauer, ?Elimination with weighted row combinations for solving linear equations and least squares problems,? Numer. Math.,7, No. 4, 338?352 (1965). · Zbl 0142.11504 · doi:10.1007/BF01436528
[421] F. L. Bauer, ?Genauigkeitsfragen bei der Lösung linearer Gleichungssysteme,? Z. Angew. Math. Mech.,46, No. 7, 409?421 (1966). · Zbl 0148.39101 · doi:10.1002/zamm.19660460702
[422] F. L. Bauer, ?Theory of norms,? Computer Sci. Dept., Stanford Univ., Tech. Rep. CS75 (1967).
[423] F. L. Bauer, ?QD-method with Newton shift,? Computer Sci. Dept., Stanford Univ., Tech. Rep. No. 56 (1967).
[424] F. L. Bauer, ?Some aspects of scaling invariance,? Colloq. Internat. Centre Nat. Rech. Scient., No. 165, 37?47 (1968). · Zbl 0209.46603
[425] F. L. Bauer, ?Remarks on optimally scaled matrices,? Numer. Math.,13, No. 1, 1?3 (1969). · Zbl 0172.18704 · doi:10.1007/BF02165268
[426] F. L. Bauer, ?Computational graphs and rounding error,? SIAM J. Numer. Anal.,11, No. 1, 87?96 (1974). · Zbl 0337.65028 · doi:10.1137/0711010
[427] F. L. Bauer, Positivity and Norms, Gatlinburg VI. Symposium on Numerical Algebra (Hopfen am See, 1974), Munchen (1974).
[428] F. L. Bauer, J. Heinhold, K. Samelson, and R. Sauer, Moderne Rechenanlagen; eine Einführung, B. G. Teubner, Stuttgart (1965). · Zbl 0131.15605
[429] F. L. Bauer and C. Reinsch, ?Inversion of positive-definite matrices by the Gauss -Jordan method,? Grundlehren Math. Wiss. Einzeldarstell.,186, 45?49 (1971).
[430] R. Baumann, ?Some new aspects of load flow calculation,? IEEE Trans. Power Appar. Systems,85, 1164?1176 (1965).
[431] R. Baumann, ?Sparseness in power systems equations,? in: Large Sparse Sets of Linear Equations, Academic Press, London-New York (1971), pp. 105?126.
[432] A. N. Beavers and E. D. Denman, ?A computational method for eigenvalues and eigenvectors of a matrix with real eigenvalues,? Numer. Math.,21, No. 5, 389?396 (1973). · Zbl 0296.65017 · doi:10.1007/BF01436489
[433] F. S. Beckman, ?The solution of linear equations by the conjugate gradient method,? in: Math. Methods for Digital Computers, Wiley, New York (1960), pp. 62?72.
[434] H. Beeck, ?Uberintervallanalytische Methoden bei linearen Gleichungssystemen mit Intervallkoeffizienten und Zusammenhänge mit der Fehleranalysis,? Diss., TU Munchen (1971).
[435] H. Beeck,?Über Struktur und Abschätzungen der Lösungsmenge von linearen Gleichungssystemen mit Intervallkoeffizienten,? Computing,10, No. 3, 231?244 (1972). · Zbl 0255.65014 · doi:10.1007/BF02316910
[436] H. Beeck, ?Charakterisierung der Lösungsmenge von Intervallgleichungssystemen,? Z. Angew. Math. Mech.,53, No. 4, T181-T182 (1973). · Zbl 0259.65048
[437] H. Beeck, ?Zur scharfen Aussenabschätzung der Lösungsmenge bei linearen Intervallgleichungssystemen,? Z. Angew. Math. Mech.,54, No. 4, 208?209 (1974). · Zbl 0311.65026 · doi:10.1002/zamm.197405412118
[438] R. Bellman, Introduction to Matrix Analysis, 2nd ed., McGraw-Hill, New York (1970). · Zbl 0216.06101
[439] R. Bellman, R. Kalaba, and J. Lockett, ?Dynamic programming and ill-conditioned linear systems,? J. Math. Anal. Appl.,10, No. 1, 206?215 (1965). · Zbl 0128.39302 · doi:10.1016/0022-247X(65)90155-1
[440] C. F. Bender and I. Shavitt, ?An iterative procedure for the calculation of the lowest real eigenvalue and eigenvector of a nonsymmetric matrix,? J. Comput. Phys.,6, No. 1, 146?149 (1970). · Zbl 0204.48203 · doi:10.1016/0021-9991(70)90014-8
[441] A. Ben-Israel, ?An iterative method for computing the generalized inverse of an arbitrary matrix,? Math. Comput.,19, No. 91, 452?455 (1965). · doi:10.1090/S0025-5718-1965-0179915-5
[442] A. Ben-Israel, ?On error bounds for generalized inverses,? SIAM J. Numer. Anal.,3, No. 4, 585?592 (1966). · Zbl 0147.13201 · doi:10.1137/0703050
[443] A. Ben-Israel, ?A note on an iterative method for generalized inversion of matrices,? Math. Comput.,20, No. 95, 439?440 (1966). · doi:10.1090/S0025-5718-66-99922-4
[444] A. Ben-Israel, ?On decompositions of matrix spaces with applications to matrix equations,? Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. e Natur.,45, Nos. 3?4, 122?128 (1968) (1969).
[445] A. Ben-Israel, ?A note of partitioned matrices and equations,? SIAM Rev.,11, No. 2, 247?250 (1969). · Zbl 0175.02402 · doi:10.1137/1011038
[446] A. Ben-Israel and A. Charnes, ?Contributions to the theory of generalized inverses,? SIAM J. Appl. Math.,11, No. 3, 667?699 (1963). · Zbl 0116.32202 · doi:10.1137/0111051
[447] A. Ben-Israel and D. Cohen, ?On iterative computation of generalized inverses and associated projections,? SIAM J. Numer. Anal.,3, No. 3, 410?419 (1966). · Zbl 0143.37402 · doi:10.1137/0703035
[448] A. Ben-Israel and Y. Ijiri, ?A report on the machine computation of the generalized inverse of an arbitrary matrix,? Carnegie Inst. Tech. Grad. School Indust. Admin., ONR Research Memo No. 110 (1963).
[449] A. Ben-Israel and S. J. Wersan, ?A least-square method for computing the generalized inverse of an arbitrary complex matrix,? Tech. Inst., Northwestern Univ., ONR Research Memo No. 61 (1962). · Zbl 0118.12104
[450] A. Ben-Israel and S. J. Wersan, ?An elimination method for computing the generalized inverse of an arbitrary complex matrix,? J. Assoc. Comput. Mach.,10, No. 4, 532?537 (1963). · Zbl 0118.12104 · doi:10.1145/321186.321197
[451] J. M. Bennett, ?Triangular factors of modified matrices,? Numer., Math.,7, No. 3, 217?221 (1965). · Zbl 0132.36204 · doi:10.1007/BF01436076
[452] W. Benning, ?Numerischer Vergleich von iterativen und directen Verfahren zur Auflösung linearer inhomogener Gleichungssysteme,? Mitt. Inst. Theor. Geod. Univ. Bonn.,11, No. 27 (1974).
[453] N. F. Benschop and H. C. Ratz, ?A mean square estimate of the generated roundoff error in constant matrix iterative processes,? J. Assoc. Comput. Mach.,18, No. 1, 48?62 (1971). · Zbl 0217.21502 · doi:10.1145/321623.321629
[454] A. Benson and R. J. Evans, ?The successive peripheral block overrelaxation method,? J. Inst. Math. Appl.,9, No. 1, 68?79 (1972). · Zbl 0235.65072 · doi:10.1093/imamat/9.1.68
[455] L. Berg, ?Über grosse Gleichungssysteme mit einer Bandmatrix,? Z. Angew. Math. Mech.,52, No. 5, 252?254 (1972). · Zbl 0254.15002 · doi:10.1002/zamm.19720520414
[456] A. Berman and R. Plemmons, ?Cones and iterative methods for best least squares solutions of linear systems,? SIAM J. Numer. Anal.,11, No. 1, 145?154 (1974). · Zbl 0244.65024 · doi:10.1137/0711015
[457] U. Bertele and F. Brioschi, ?On the theory of the elimination process,? J. Math. Anal. Appl.,35, 48?57 (1971). · Zbl 0233.90024 · doi:10.1016/0022-247X(71)90234-4
[458] G. Birkhoff, R. S. Varga, and D. M. Young, ?Alternating direction implicit methods,? in: Advances in Computers, Vol. 3, Academic Press, New York (1962), pp. 189?273. · Zbl 0111.31402
[459] L. Bittner, ?Über ein mehrstufiges Iterationsverfahren zur Lösung von linearen Gleichungen,? Numer. Math.,6, No. 3, 161?180 (1964). · Zbl 0123.32102 · doi:10.1007/BF01386065
[460] L. Bittner, ?Die Methode der sukzessiven Gauss-Jordan-Elimination, das Austauschverfahren, zur Invertierung, Rangbestimmung, Gleichungsauflösung und Determinaatenberechnung,? in: D. K. Faddejew and W. N. Faddejewa, Numerische Methoden der linearen Algebra, Veb Deutscher Verlag der Wissenschaften, Berlin (1973), pp. 765?775.
[461] A. Bjerhammer, ?A generalized matrix algebra,? Kungl. Tekh. Hogsk. Handl., Stockholm, No. 124 (1958).
[462] O. E. Bjønlund and T. L. Johnson, ?The hypermatrix QR factorization. A hypermatrix generalization of Householder’s method,? ISD-Rept., No. 112 (1971).
[463] A. Björck, ?Solving linear least squares problems by Gram-Schmidt orthogonalization,? BIT,7, No. 1, 1?21 (1967). · Zbl 0183.17802 · doi:10.1007/BF01934122
[464] A. Björck, ?Iterative refinement of linear least squares solutions. I,? BIT,7, No. 4, 257?278 (1967). · Zbl 0159.20404 · doi:10.1007/BF01939321
[465] A. Björck, ?Iterative refinement of linear least squares solutions. II,? BIT,8, No. 1, 8?30 (1968). · Zbl 0177.43204 · doi:10.1007/BF01939974
[466] A. Björck and C. Bowie, ?An iterative algorithm for computing the best estimate of an orthogonal matrix,? SIAM J. Numer. Anal.,8, No. 2, 358?364 (1971). · Zbl 0221.65075 · doi:10.1137/0708036
[467] A. Björck and G. Golub, ?Iterative refinements of linear least squares solutions by Householder transformations,? Computer Sci. Dept., Stanford Univ., Tech. Rep. CS 83 (1968).
[468] J. W. Blattner, ?On the convergence of a certain matrix iteration,? Bul. Inst. Politeh. Iasi,10, Nos. 3?4, 43?46 (1964).
[469] M. M. Blevins and G. W. Stewart, ?Calculating the eigenvectors of diagonally dominant matrices,? J. Assoc. Comput. Mach.,21, No. 2, 261?271 (1974). · Zbl 0297.65026 · doi:10.1145/321812.321821
[470] E. K. Blum, ?Computation of proper values of a symmetric matrix by the convergent gradient procedure,? ICC Research Rep. No. 6514 (1965).
[471] E. Bodewig, ?L’equation minimale d’une matrice,? Bull. Sci. Math.,91, Nos. 3?4, 129?130 (1967) (1968). · Zbl 0159.32302
[472] P. T. Boggs, ?A new algorithm for the Chebyshev solution of overdetermined linear systems,? Math. Comput.,28, No. 125, 203?218 (1974). · Zbl 0293.65025 · doi:10.1090/S0025-5718-1974-0334482-3
[473] Z. Bohte, ?Numerical solution of the inverse algebraic eigenvalue problem,? Comput. J.,10, No. 4, 385?388 (1968). · Zbl 0167.45303 · doi:10.1093/comjnl/10.4.385
[474] Z. Bohte, ?Rounding errors in the Gaussian elimination for band systems,? Publs. Dept. Math., Univ. Ljubljana Inst. Math. Phys. and Mech.,6, 7?35 (1974). · Zbl 0283.65010
[475] C. de Boor and J. R. Rice, ?Chebyshev approximation by all (X-ri)/(X+si) and application to ADI iteration,? SIAM J. Appl. Math.,11, No. 1, 159?169 (1963). · Zbl 0116.04503 · doi:10.1137/0111012
[476] C. de Boor and J. R. Rice, ?Tensor products and commutative matrices,? SIAM J. Appl. Math.,12, No. 4, 892?896 (1964). · Zbl 0156.26802 · doi:10.1137/0112077
[477] J. Boothroyd, ?The symmetric matrix eigenproblem ? Jacobi’s method revisited,? Austral. Comput. J.1, 86?94 (1968).
[478] J. Boothroyd, ?The QR algorithm for symmetric tridiagonal matrices using a semiimplicit shift of origin,? Austral. Comput. J.,2, No. 2, 55?60 (1970). · Zbl 0239.65038
[479] I. Boroch and A. S. Fraenkel, ?Exact solutions of linear equations with rational coefficients by congruence techniques,? Math. Comput.,20, No. 93, 107?112 (1966). · doi:10.1090/S0025-5718-1966-0187379-1
[480] E. Boros, ?Asupra inversei generalizate a unei matrici EPr,? An. Univ. Timisoara. Ser. Sti. Mat.-Fiz.,2, 33?38 (1964).
[481] E. Boros, ?Asupra unor proprietati ale matricilor Epr,? An. Univ. Timisoara. Ser. Sti. Mat.-Fiz.,3, 77?84 (1965).
[482] L. Bosset, ?Quelques experiences numeriques sur la methode de Rutishauser pour le calcul des valeurs propres,? 3-e Congr. Calcul et Traitem. Inform. AFCALTI, Toulouse, 1963, Paris, 123?129 (1965).
[483] R. Bouldin, ?The pseudoinverse of a product,? SIAM J. Appl. Math.,24, No. 4, 489?495 (1973). · Zbl 0236.47007 · doi:10.1137/0124051
[484] T. L. Boullion and P. L. Odell, Generalized Inverse Matrices, Wiley-Interscience, New York (1971). · Zbl 0223.15002
[485] H. J. Bowdler, R. S. Martin, G. Peters, and J. H. Wilkinson, ?Solution of real and complex systems of linear equations,? Numer. Math.,8, No. 3, 217?234 (1966). · Zbl 0158.33805 · doi:10.1007/BF02162559
[486] H. J. Bowaler, R. S. Martin, C. Reinsch, and J. H. Wilkinson, ?The QR and QL algorithms for symmetric matrices,? Numer. Math.,11, No. 4, 293?306 (1968). · Zbl 0162.46803 · doi:10.1007/BF02166681
[487] W. W. Bradbury and R. Fletcher, ?New iterative methods for solution of the eigenproblem,? Numer. Math.,9, No. 3, 259?267 (1966). · Zbl 0202.43502 · doi:10.1007/BF02162089
[488] D. Braess, ?Die Konstruktion monotoner Iterationsfolgen zur Lösungseinschliessung bei linearen Gleichungssystemen,? Arch. Ration. Mech. Anal.,9, No. 2, 97?106 (1962). · Zbl 0118.12103 · doi:10.1007/BF00253336
[489] D. Braess, ?Monotone iterationsfolgen bei Gleichungssystemen mit fehlerhaften Koeffizienten und Iterationsbeschleunigung,? Numer. Math.,7, No. 1, 32?41 (1965). · Zbl 0125.35904 · doi:10.1007/BF01397971
[490] D. Braess, ?Die Berechnung der Fehlergrenzen bei linearen Gleichungssystemen mit fehlerhaften Koeffizienten,? Arch. Ration. Mech. Anal.,19, No. 1, 74?80 (1965). · Zbl 0134.32703 · doi:10.1007/BF00252280
[491] A. Brameller and K. L. Lo, ?The application of diakoptics and the escalator method to the solution of very large eigenvalue problems,? Int. J. Numer. Meth. Eng.,2, No. 4, 535?549 (1970). · Zbl 0253.65022 · doi:10.1002/nme.1620020407
[492] Th. Brannström, ?On the method of Lanczos for finding eigenvalues of unsymmetric matrices,? Rep. UMINF 44.73 (1973).
[493] H. Brass, ?Ein Kapitel aus der Theorie der linearen Gleichungssysteme,? Math.-Phys. Semesterber,17, No. 1, 97?108 (1970). · Zbl 0207.15601
[494] R. K. Brayton, F. G. Gustavson, and R. A. Willoughby, ?Some results on sparse matrices,? Math. Comput.,24, No. 112, 937?954 (1970). · doi:10.1090/S0025-5718-1970-0275643-8
[495] J. L. Brenner and J. de Pilis, ?Partitioned matrices and Seidel convergence,? Numer. Math.,19, No. 1, 76?80 (1972). · Zbl 0223.65009 · doi:10.1007/BF01395932
[496] R. P. Brent, ?Error analysis of algorithms for matrix multiplication and triangular decomposition using Winograd’s identity,? Numer. Math.,16, No. 2, 145?156 (1970). · Zbl 0193.11902 · doi:10.1007/BF02308867
[497] C. Brezinski, ?Methods of acceleration of convergence in numerical analysis,? Thesis. Univ. Grenoble (1971).
[498] C. Brezinski, ?Theoremes de convergence pour l’?-algorithme,? C. R. Acad. Sci.,274, No. 1, A94-A96 (1972). · Zbl 0248.65005
[499] C. Brezinski, ?Etude de la convergence de l’?-algorithme,? C. R. Acad. Sci.,274, No. 14, A1120-A1123 (1972). · Zbl 0248.65006
[500] C. Brezinski, ?Some results in the theory in the vector ?-algorithm,? Linear Algebra Appl.,8, No. 1, 77?86 (1974). · Zbl 0273.65026 · doi:10.1016/0024-3795(74)90010-X
[501] Ole Einar Brönlund, ?Die simultane Verbesserung einer beliebigen Anzahl genäherter Eigenvektoren von hermiteschen Matrizen,? Diss. Dokt. Ing. Univ. Stuttgart (1973).
[502] C. G. Broyden, ?Some generalizations of the theory of successive overrelaxation,? Numer. Math.,6, No. 4, 269?284 (1964). · Zbl 0244.65021 · doi:10.1007/BF01386075
[503] C. G. Broyden, ?On convergence criteria for the method of successive overrelaxation,? Math. Comput.,18, No. 85, 136?141 (1964). · Zbl 0115.34302 · doi:10.1090/S0025-5718-1964-0158527-2
[504] C. G. Broyden, ?Some aspects of consistent ordering,? Numer. Math.,12, No. 1, 47?56 (1968). · Zbl 0181.17204 · doi:10.1007/BF02170996
[505] C. G. Broyden, ?Some condition-number bounds for the Gaussian elimination process,? J. Inst. Math. Appl.,12, No. 3, 273?286 (1973). · Zbl 0268.65028 · doi:10.1093/imamat/12.3.273
[506] C. G. Broyden, ?Error propagation in numerical processes,? J. Inst. Math. Appl.,14, No. 2, 131?140 (1974). · Zbl 0288.65021 · doi:10.1093/imamat/14.2.131
[507] C. G. Broyden and F. Ford, ?An algorithm for the solution of certain kinds of linear equations,? Numer. Math.,8, No. 4, 307?323 (1966). · Zbl 0158.33902 · doi:10.1007/BF02162976
[508] M. L. Buchanan, ?Norms of powers of matrices in a special class,? SIAM J. Numer. Anal.,3, No. 4, 616?623 (1966). · Zbl 0153.46105 · doi:10.1137/0703054
[509] A. Buckley, ?A note on matrices A=I+H, H skew-symmetric,? Z. Angew. Math. Mech.,54, No. 2, 125?126 (1974). · Zbl 0283.15006 · doi:10.1002/zamm.19740540209
[510] G. Buffoni, ?Evaluation of eigensolutions of discrete space diffusion equation,? Calcolo,4, 169?177 (1967). · Zbl 0162.20702 · doi:10.1007/BF02576732
[511] T. T. Bui Thui and G. Hunter, ?The significant order of symmetric tridiagonal matrices,? J. Inst. Math. Appl.,14, No. 3, 293?301 (1974). · Zbl 0295.15005 · doi:10.1093/imamat/14.3.293
[512] J. R. Bunch, ?On direct methods for solving symmetric systems of linear equations,? Ph. D. Thesis, Univ. California, Berkeley (1969).
[513] J. R. Bunch, ?Analysis of the diagonal pivoting method,? SIAM J. Numer. Anal.,8, No. 4, 656?680 (1971). · Zbl 0222.65039 · doi:10.1137/0708061
[514] J. R. Bunch, ?Equilibration of symmetric matrices in the max-norm,? J. Assoc. Comput. Mach.,18, No. 4, 566?572 (1971). · Zbl 0242.65045 · doi:10.1145/321662.321670
[515] J. R. Bunch, ?Partial pivoting strategies for symmetric matrices,? SIAM J. Numer. Anal.,11, No. 3, 521?528 (1974). · Zbl 0253.65024 · doi:10.1137/0711043
[516] J. R. Bunch and J. E. Hopcroft, ?Triangular factorization and inversion by fast matrix multiplication,? Math. Comput.,28, No. 125, 231?236 (1974). · Zbl 0276.15006 · doi:10.1090/S0025-5718-1974-0331751-8
[517] J. R. Bunch and B. N. Parlett, ?Direct methods for solving symmetric indefinite systems of linear equaequations,? SIAM J. Numer. Anal.,8, No. 4, 639?655 (1971). · Zbl 0222.65038 · doi:10.1137/0708060
[518] P. A. Businger, ?Matrix scaling with respect to the maximum-norm, the sum-norm, and the euclidean norm,? Univ. Texas Comput. Center, TNN71 (1967).
[519] P. A. Businger, ?Matrices which can be optimally scaled,? Numer. Math.,12, No. 4, 346?348 (1968). · Zbl 0167.15603 · doi:10.1007/BF02162515
[520] P. A. Businger, ?Extremal properties of balanced tridiagonal matrices,? Math. Comput.,23, No. 105, 193?195 (1969). · Zbl 0177.20202 · doi:10.1090/S0025-5718-1969-0238476-6
[521] P. A. Businger, ?Reducing a matrix to Hessenberg form,? Math. Comput.,23, No. 108, 819?821 (1969). · Zbl 0183.43902 · doi:10.1090/S0025-5718-1969-0258255-3
[522] P. A. Businger, ?Updating a singular value decomposition,? BIT,10, No. 3, 376?385 (1970). · doi:10.1007/BF01934207
[523] P. A. Businger, ?Numerically stable deflation of Hessenberg and symmetric tridiagonal matrices,? BIT,11, No. 3, 262?270 (1971). · Zbl 0226.65028 · doi:10.1007/BF01931807
[524] P. A. Businger, ?Monitoring the numerical stability of Gaussian elimination,? Numer. Math.,16, No. 4, 360?361 (1971). · Zbl 0194.18103 · doi:10.1007/BF02165006
[525] P. A. Businger and G. H. Golub, ?Linear least squares solutions by Householder transformations,? Numer. Math.,7, No. 3, 269?276 (1965). · Zbl 0142.11503 · doi:10.1007/BF01436084
[526] H. J. Buurema, ?A geometric proof of convergence for the QR-method,? Groningen, Math. Inst., Rep. TW-62 (1968). · Zbl 0206.46304
[527] H. J. Buurema, ?A geometric proof of convergence for the QR method,? Thesis, Rijksuniversiteit Groningen (1970). · Zbl 0206.46304
[528] J. Bystry, ?Inverze matice pomoci vlastnich cisel a vlastnich vektorn,? Sb. Vojen. Akad. A. Zapotockeho,B18, No. 1, 75?82 (1970).
[529] J. A. Cadzow, ?A finite algorithm for the minimuml ? solution to a system of consistent linear equations,? SIAM J. Numer. Anal.,10, No. 4, 607?617 (1973). · Zbl 0261.65033 · doi:10.1137/0710053
[530] J. A. Cadzow, ?An efficient algorithmic procedure for obtaining a minimum l-norm solution to a system of consistent linear equations,? SIAM J. Numer. Anal.,11, No. 6, 1151?1165 (1974). · Zbl 0292.65015 · doi:10.1137/0711087
[531] J. Caffrey, ?Another test matrix for determinants and inverses,? Commun. ACM,6, No. 6, 310 (1963). · doi:10.1145/366604.366618
[532] D. A. Calahan and W. J. McCalla, ?Eigenvalue methods for sparse matrices,? in: Sparse Matrices and Applications, Plenum Press, New York-London (1972), pp. 25?30.
[533] G. Cantin, ?An equation solver of very large capacity,? Int. J. Numer. Meth. Eng.,3, 379?388 (1971). · Zbl 0252.68013 · doi:10.1002/nme.1620030307
[534] J. Carpentier, ?Ordered eliminations,? Proc. Power Systems Comput. Conf. London (1963).
[535] J. Carpentier, ?Eliminations ordonnees un processus diminuant le volume des calculs dans la resolution des systemes lineaires a matrice creuse,? 3-e Congr. Calcul et Traitem. Inform. AFCALTI, Toulouse, 1963, Paris, 63?70 (1965).
[536] B. A. Carre, ?The determination of the optimum accelerating factor for successive over-relaxation,? Comput. J.,4, No. 1, 73?78 (1961). · Zbl 0098.31405 · doi:10.1093/comjnl/4.1.73
[537] Manas Chanda and Syamal Kumar Sen, ?A process for the selection of overrelaxation factor ? and the related computation for Ax=b,? J. Indian Inst. Sci.,53, No. 2, 111?119 (1971).
[538] S. Charmonman, ?An efficient algorithm for inverting a block-symmetric matrix,? Math. Comput.,21, No. 100, 715?717 (1967). · Zbl 0161.35403 · doi:10.1090/S0025-5718-67-99906-1
[539] S. Charmonman and R. S. Julius, ?Explicit inverses and condition numbers of certain circulants,? Math. Comput.,22, 428?430 (1968). · Zbl 0261.15002 · doi:10.1090/S0025-5718-1968-0226831-9
[540] B. A. Chartres, ?Controlled precision calculations and the Danilewsky method,? Div. Appl. Math., Brown Univ. (1964).
[541] B. A. Chartres and J. C. Geuder, ?Computable error bounds for direct solution of linear equations,? J. Assoc. Comput. Mach.,14, No. 1, 63?71 (1967). · Zbl 0153.46103 · doi:10.1145/321371.321376
[542] F. Chatelin-Laborde, ?Perturbation d’une matrice hermitienne ou normale,? Numer. Math.,17, No. 4, 318?337 (1971). · Zbl 0221.65072 · doi:10.1007/BF01420901
[543] F. Chatelin-Laborde, ?Error bounds in QR and Jacobi algorithms applied to Hermitian or normal matrices,? Proc. IFIP Congr. 71, Ljubljana, 1971, North-Holland, Amsterdam-London (1972). · Zbl 0254.65026
[544] F. Chatelin-Laborde, ?Sur la convergence de l’algorithme QR pour une matrice hermitienne,? Rev. Franc. Automat., Inf., Rech. Oper.,7, No. R-1, 57?61 (1973). · Zbl 0259.65044
[545] D. Chazan and W. Miranker, ?Chaotic relaxation,? Linear Algebra Appl.,2, No. 2, 199?222 (1969). · Zbl 0225.65043 · doi:10.1016/0024-3795(69)90028-7
[546] Fan Y. Chen, ?An explicit algorithm for solving linear equations of Jacobi type,? Int. J. Numer. Meth. Eng.,8, No. 3, 659?661 (1974). · Zbl 0284.65025 · doi:10.1002/nme.1620080318
[547] H. C. Chen and D. K. Cheng, ?A useful matrix inversion formula and its applications,? Proc. IEEE,55, No. 5, 705?706 (1967). · doi:10.1109/PROC.1967.5649
[548] Richard M.-M. Chen, ?New matrix inversion algorithms based on exchange method,? IEEE Trans. Comput.,22, No. 10, 885?890 (1973). · Zbl 0265.65017 · doi:10.1109/T-C.1973.223613
[549] Y. T. Chen, ?Permutation of irreducible sparse matrices to upper triangular forms,? J. Inst. Math. Appl.,10, No. 1, 15?18 (1972). · Zbl 0246.65017 · doi:10.1093/imamat/10.1.15
[550] Y. T. Chen and R. P. Tewarson, ?On the fill-in when sparse vectors are orthonormalized,? Computing,9, No. 1, 53?56 (1972). · Zbl 0234.65049 · doi:10.1007/BF02236376
[551] Y. T. Chen and R. P. Tewarson, ?On the optimal choice of pivots for the Gaussian elimination,? Computing,9, No. 3, 245?250 (1972). · Zbl 0253.65013 · doi:10.1007/BF02246733
[552] K. Y. Cheng, ?Note on minimizing the bandwidth of sparse, symmetric matrices,? Computing,11, No. 1, 27?30 (1973). · Zbl 0257.65041 · doi:10.1007/BF02239468
[553] K. Y. Cheng, ?Minimizing the bandwidth of sparse symmetric matrices,? Computing,11, No. 2, 103?110 (1973). · Zbl 0263.65049 · doi:10.1007/BF02252900
[554] M. R. Chidambara, ?On the inverses of certain matrices,? IEEE Trans. Autom. Control,12, No. 2, 214?215 (1967). · doi:10.1109/TAC.1967.1098550
[555] J. S. Chipman, ?On least squares with insufficient observations,? J. Am. Statist. Assoc,59, No. 308, 1078?1111 (1964). · Zbl 0144.42401 · doi:10.1080/01621459.1964.10480751
[556] R. Chmurny, ?Singularita matic a stabilita inverznych matic pouzivanych pri technickych vypoctoch,? Strojnicky Casop.,18, No. 6, 565?573 (1967).
[557] D. Roy Choudhury, ?Algorithm for power of companion matrix and its application,? IEEE Trans. Autom. Control.,18, No. 2, 179?180 (1973). · doi:10.1109/TAC.1973.1100268
[558] T. S. Chow, ?A class of Hessenberg matrices with known eigenvalues and inverses,? SIAM Rev.,11, No. 3, 391?395 (1969). · Zbl 0185.07803 · doi:10.1137/1011065
[559] T. S. Chow and J. S. Kowalik, ?Computing with sparse matrices,? Int. J. Numer. Meth. Eng.,7, No. 2, 211?223 (1973). · Zbl 0263.65041 · doi:10.1002/nme.1620070210
[560] T. S. Chow and H. W. Milnes, ?Concerning the exceptional case in Hessenberg’s method,? Indag. Math.,17, No. 2, 69?76 (1967).
[561] H. Chu, ?A method of Samuels on and minimal polynomials,? J. Math. Anal. Appl.,21, No. 2, 396?404 (1968). · Zbl 0251.65030 · doi:10.1016/0022-247X(68)90223-0
[562] M. E. Churchill, ?A sparse matrix procedure for power systems analysis programs,? in: Large Sparse Sets of Linear Equations, Academic Press, London-New York (1971), pp. 127?137.
[563] Gianfranco Cimmino, ?Un metodo Monte Carlo per la risoluzione numerica dei sistemi di equazioni lineari,? Atti Accad. Sci. Ist. Bologna. Cl. Sci. Fis. Rend.,2, Nos. 1?2, 39?44 (1967).
[564] A. K. Cline, ?An elimination method for the solution of linear least squares problems,? SIAM J. Numer. Anal.,10, No. 2, 283?289 (1973). · Zbl 0253.65023 · doi:10.1137/0710027
[565] R. E. Cline, ?Note on the generalized inverse of the product of matrices,? SIAM Rev.,6, No. 1, 57?58 (1964). · Zbl 0121.26105 · doi:10.1137/1006007
[566] R. E. Cline, ?Representations for the generalized inverse of a partitioned matrix,? SIAM J. Appl. Math.,12, No. 3, 588?600 (1964). · Zbl 0166.29902 · doi:10.1137/0112050
[567] R. E. Cline, ?A class of matrices to test inversion procedures,? Commun. ACM,7, No. 12, 724?725 (1964). · Zbl 0126.32201 · doi:10.1145/355588.365132
[568] R. E. Cline, ?Representations for the generalized inverse of sums of matrices,? SIAM J. Numer. Anal.,2, No. 1, 99?114 (1965). · Zbl 0142.26904
[569] R. E. Cline and T. N. E. Greville, ?An extension of the generalized inverse of a matrix,? SIAM J. Appl. Math.,19, No. 4, 682?688 (1970). · Zbl 0236.15010 · doi:10.1137/0119069
[570] M. Clint and A. Jennings, ?The evaluation of eigenvalues and eigenvectors of real symmetric matrices by simultaneous iteration,? Comput. J.,13, No. 1, 76?80 (1970). · Zbl 0194.18203 · doi:10.1093/comjnl/13.1.76
[571] M. Clint and A. Jennings, ?A simultaneous iteration method for the unsymmetric eigenvalue problem,? J. Inst. Math. Appl.,8, No. 1, 111?121 (1971). · Zbl 0221.65070 · doi:10.1093/imamat/8.1.111
[572] L. Collatz, Eigenwertaufgaben mit Technischen Anwendungen, Geest and Portig, Leipzig (1963).
[573] L. Collatz, Funktionalanalysis und Numerische Mathematik, Vol. XVI, Springer-Verlag, Berlin (1964). · Zbl 0139.09802
[574] G. Collombat, ?Une classe de matrices tri-diagonales-tests,? Rev. Franc. Automat., Inf., Rech. Oper.,6, No. R-2, 77?79 (1972). · Zbl 0251.15009
[575] T. M. T. Coolen and P. J. van der Houwen, ?On the aceleration of Richardson’s method. IV. A nonsymmetrical case,? Math. Centrum Amsterdam AFD, Toegepaste Wisk. Rep. TW-109 (1968).
[576] F. J. Corbato, ?On the coding of Jacobi’s method for computing eigenvalues and eigenvectors of real symmetric matrices,? J. Assoc. Comput. Mach.,10, No. 2, 123?125 (1963). · Zbl 0117.11201 · doi:10.1145/321160.321161
[577] C. R. Crawford, ?Reduction of a band-symmetric generalized eigenvalue problem,? Commun. ACM,16, No. 1, 41?44 (1973). · Zbl 0247.65025 · doi:10.1145/361932.361943
[578] L. Crone, ?The singular value decomposition of matrices and cheap numerical filtering of systems of linear equations,? J. Franklin Inst.,294, No. 2, 133?136 (1972). · Zbl 0295.65030 · doi:10.1016/0016-0032(72)90128-7
[579] T. R. Crossley and B. Porter, ?Eigenvalue and eigenvector sensitivities in linear systems theory,? Int. J. Control,10, No. 2, 163?170 (1969). · Zbl 0175.09401 · doi:10.1080/00207176908905813
[580] J. Crouzeix, ?Statistical study of propagated errors in the solution of linear systems,? Thesis, Univ. Clermont (1968).
[581] J. Crouzeix, ?Etude de l’erreur d’arrondi dans la resolution de systemes lineaires par des methodes iteratives,? Rev. Franc. Inform. et Rech. Oper.,5, No. R-2, 100?106 (1971).
[582] C. W. Cryer, ?Pivot size in Gaussian elimination,? Numer. Math.,12, No. 4, 335?345 (1968). · Zbl 0172.18801 · doi:10.1007/BF02162514
[583] K. Csebfalvi, ?Über Iterationsverfahren zur Lösung linearer Gleichungssysteme,? Elektron. Datenverarb.,7, No. 1, 44?46 (1965). · Zbl 0136.12704
[584] A. R. Curtis and J. K. Reid, ?Fortran subroutines for the solution of linear equations,? Res. Group, U.K.Atom. Energy Auth., No. AERE-R6844 (1971).
[585] A. R. Curtis and J. K. Reid, ?The solution of large sparse unsymmetric systems of linear equations,? J. Inst. Math. Appl.,13, No. 3, 344?353 (1971). · Zbl 0229.65032 · doi:10.1093/imamat/8.3.344
[586] A. R. Curtis and J. K. Reid, ?The solution of large sparse unsymmetric systems of linear equations,? Proc. IFIP Congr. 71, Ljubljana, 1971, Vol. 2, 1240?1245, North-Holland, Amsterdam-London (1972). · Zbl 0229.65032
[587] A. R. Curtis and J. K. Reid, ?On the automatic scaling of matrices for Gaussian elimination,? J. Inst. Math. Appl.,10, No. 1, 118?124 (1972). · Zbl 0249.65026 · doi:10.1093/imamat/10.1.118
[588] J. H. Curtiss, ?Monte Carlo methods for the iteration of linear operators,? J. Math. Phys.,32, No. 4, 209?232 (1954). · Zbl 0055.11301 · doi:10.1002/sapm1953321209
[589] E. Guthill, ?Several strategies for reducing the bandwidth of matrices,? in: Sparse Matrices and Applications, Plenum Press, New York-London (1972), pp. 157?166.
[590] E. H. Guthill and J. McKee, ?Reducing the bandwidth of sparse symmetric matrices,? Proc. 24th ACM Nat. Conf., New York, N. Y., 157?172 (1969).
[591] B. Cvetcov, ?On the least squares adjustment of arbitrary inconsistent linear equations,? Surv. Rev.,17, No. 128, 89?95 (1963). · doi:10.1179/sre.1963.17.128.89
[592] G. Dahlquist, S. Eisenstat, and G. H. Golub, ?Bounds for the error of linear systems of equations using the theory of moments,? J. Math. Anal. Appl.,37, No. 1, 151?166 (1972). · Zbl 0238.65012 · doi:10.1016/0022-247X(72)90264-8
[593] G. D’Amico, S. Nevaloro, and A. Tiramani, ?Two time-saving procedures for the solution of large sparse sets of linear equations,? Int. Comput. Symp., Venice (1972).
[594] J. W. Daniel, ?Convergence of the conjugate gradient method with computationally convenient modifications,? Numer. Math.,10, No. 2, 125?131 (1967). · Zbl 0178.18302 · doi:10.1007/BF02174144
[595] G. B. Dantzig, R. P. Harvey, R. D. McKhight, and S. S. Smith, ?Sparse matrix techniques in two mathematical programming codes,? in: Sparse Matrix Proceedings, R. A. Willoughby (ed.), RA 1, No. 11707, IBM Corp.,Thomas J. Watson Res. Center, Yorktown Heights, New York (1969), pp. 85?99.
[596] C. Davis, ?The rotation of eigenvectors by a perturbation,? J. Math. Anal. Appl.,6, No. 2, 159?173 (1963). · Zbl 0115.10403 · doi:10.1016/0022-247X(63)90001-5
[597] C. Davis, ?The rotation of eigenvectors by a perturbation. II,? J. Math. Anal. Appl.,11, Nos. 1?3, 20?27 (1965). · Zbl 0138.08001 · doi:10.1016/0022-247X(65)90066-1
[598] C. Davis and W. M. Kahan, ?The rotation of eigenvectors by a perturbation. III,? SIAM J. Numer. Anal.,7, No. 1, 1?46 (1970). · Zbl 0198.47201 · doi:10.1137/0707001
[599] H. P. Decell, ?An alternate form of the generalized inverse of an arbitrary complex matrix,? SIAM Rev.,7, No. 3, 356?358 (1965). · Zbl 0131.01502 · doi:10.1137/1007070
[600] H. P. Decell, ?An application of the Cayley-Hamilton theorem to generalized matrix inversion,? SIAM Rev.,7, No. 4, 526?528 (1965). · Zbl 0178.35504 · doi:10.1137/1007108
[601] T. J. Dekker, Evaluation of Determinants, Solution of Systems of Linear Equations and Matrix Inversion, Math. Centrum, Amsterdam, Rekanafdeling (1963), Chap. III. · Zbl 0125.07904
[602] T. J. Dekker and J. F. Traub, ?The shifted QR algorithm for Hermitian matrices,? Linear Algebra Appl.,4, No. 2, 137?154 (1971). · Zbl 0214.41005 · doi:10.1016/0024-3795(71)90035-8
[603] T. J. Dekker and J. F. Traub, ?An analysis of the shifted LR algorithm,? Numer. Math.,17, No. 3, 179?188 (1971). · Zbl 0248.65023 · doi:10.1007/BF01436374
[604] R. DeMeersman, ?Geometric meaning of the method of Golub and Kahan for the calculation of the singular values of a matrix,? Bull. Soc. Math. Belg.,22, No. 2, 146?154 (1970).
[605] H. H. Denman and R. C. W. Ettinger, ?Note on latent roots and vectors of segments of the Hubert matrix,? Math. Comput.,16, No. 79, 370?371 (1962). · Zbl 0101.33803
[606] H. H. Denman and J. P. Porzak, ?Evaluation of error measures, condition numbers and error bounds for certain matrices,? Industr. Math.,16, No. 1, 23?38 (1966).
[607] Leroy J. Derr, ?Inversion of isoclinal matrices,? Math. Comput.,26, No. 119, 719?721 (1972). · Zbl 0258.65034 · doi:10.1090/S0025-5718-1972-0327016-9
[608] L. Derwidue, ?Synthese des methodes iteratives de resolution des systemes algebriques lineaires,? Coll. Calc. Numer. et Math. Appl., Lille, 1964, Paris, 63?82 (1967).
[609] J. Descloux, ?Note on the round-off errors in iterative processes,? Math. Comput.,17, No. 81, 18?27 (1963). · Zbl 0114.32101 · doi:10.1090/S0025-5718-1963-0152102-0
[610] T. Desperat and A. Kielbasinski, ?Algorytm najlepszej strategii rozwiazymania rownan liniowych o macierzy symetrycznej dodatnio okreslonej specjalnego typu,? Zast. Mat.,9, No. 3, 261?273 (1968).
[611] E. Deutsch, ?Matricial norms,? Numer. Math.,16, No. 1, 73?84 (1970). · Zbl 0188.07701 · doi:10.1007/BF02162408
[612] E. Deutsch, ?Matricial norms and the zeros of polynomials,? Linear Algebra Appl.,3, 483?489 (1970). · Zbl 0206.35801 · doi:10.1016/0024-3795(70)90038-8
[613] E. Deutsch, ?On vectorial norms and pseudonorms,? Proc. Am. Math. Soc.,28, No. 1, 18?24 (1971). · Zbl 0209.43104 · doi:10.1090/S0002-9939-1971-0271702-7
[614] E. Deutsch, ?On matricial norms subordinate to vectorial norms,? Math. Z.,122, 142?150 (1971). · Zbl 0214.04801 · doi:10.1007/BF01110088
[615] J. C. Dickson, ?Finding permutation operations to produce a large triangular submatrix,? 28th Nat. Meeting of OR Soc. America, Houston, Texas (1965).
[616] D. Z. Dokovic, ?On the generalized inverse for matrices,? Glas. Mat.-Fiz. Astron.,20, Nos. 1?2, 51?55 (1965).
[617] J. D. P. Donnelly, ?Periodic chaotic relaxation,? Linear Algebra Appl.,4, No. 2, 117?128 (1971). · Zbl 0213.16306 · doi:10.1016/0024-3795(71)90033-4
[618] E. Dotzauer, ?Ein Iterationsverfahren zur Umordnung von Matrizen eines speziellen Typs auf Dreiecksgestalt,? Elektron. Rechenanlag.,5, No. 5, 203?210 (1963). · Zbl 0143.37501
[619] A. Douglas, ?Examples concerning efficient strategies for Gaussian elimination,? Computing,8, Nos. 3?4, 382?394 (1971). · Zbl 0231.65032 · doi:10.1007/BF02234118
[620] J. Douglas, A. O. Garder, and C. Pearcy, ?Multistage alternating direction methods,? SIAM J. Numer. Anal.,3, No. 4, 570?581 (1966). · Zbl 0168.13403 · doi:10.1137/0703048
[621] J. Douglas and J. F. Gunn, ?A general formulation of alternating direction methods. Part I. Parabolic and hyperbolic problems,? Numer. Math.,6, No. 5, 428?453 (1964). · Zbl 0141.33103 · doi:10.1007/BF01386093
[622] J. Douglas, R. B. Kellog, and R. S. Varga, ?Alternating direction iteration methods for n space variables,? Math. Comput.,17, No. 83, 279?282 (1963).
[623] J. Douglas and C. Pearcy, ?On convergence of alternating direction procedure in the presence of singular operators,? Numer. Math.,5, No. 2, 175?184 (1963). · Zbl 0115.34701 · doi:10.1007/BF01385888
[624] A. Doust and V. E. Price, ?The latent roots and vectors of a singular matrix,? Comput. J.,7, No. 3, 222?227 (1964). · Zbl 0131.34001 · doi:10.1093/comjnl/7.3.222
[625] A. Dragomir, ?Asupra inversei generalizate a unei matrici,? An. Univ. Timisoara Ser. Sti. Mat.-Fiz.,3, 123?128 (1965).
[626] E. D’Sylva and G. A. Miles, ?The S. S. O. R. iteration scheme for equations with ?1 ordering,? Comput. J.,6, No. 4, 366?367 (1964). · Zbl 0134.32704 · doi:10.1093/comjnl/6.4.366
[627] A. Dubrulle, ?A short note on the implicit QL algorithm for symmetric tridiagonal matrices,? Numer. Math.,15, No. 5, 450 (1970). · Zbl 0197.43001 · doi:10.1007/BF02165514
[628] A. Dubrulle, ?Solution of the complete symmetric eigenproblem in a virtual memory environment,? IBM J. Res. Develop.,16, No. 6, 612?616 (1972). · Zbl 0405.65013 · doi:10.1147/rd.166.0612
[629] M. Duc-Jacquet, ?Sur certains algorithmes de calcul lineaire utilisant des sommes de matrices de rang peu eleve,? Rev. Franc. Inform. et Rech. Oper.,4, No. R-1, 61?80 (1970). · Zbl 0204.48101
[630] W. Dück, ?Matrizeneigenwertprobleme mit quadratischer Parameterabhangigkeit,? Wiss. Z. Hochsch. Archit. Bauwesen Weimar,11, No. 1, 85?88 (1964).
[631] W. Dück, ?Einzelschrittverfahren zur Matrizeninversion,? Z. Angew. Math. Mech.,44, Nos. 8?9, 401?403 (1964). · Zbl 0149.36705 · doi:10.1002/zamm.19640440813
[632] W. Dück, ?Numerische Behandlung von Matrizeneigenwert-problemen mit quadratischer Parameterabhängigkeit. Teil II,? Wiss. Z. Hochsch. Archit. Bauwesen Weimar,12, No. 3, 207?214 (1965).
[633] W. Dück, ?Fehlerabschatzungen für gewisse Iterationsalgorithmen zur Matrizeninversion,? Wiss. Z. Hochsch. Archit. Bauwesen Weimar,12, Nos. 5?6, 511?514 (1965).
[634] W. Dück, ?Iterative Verfahren und Abänderungsmethoden zur Inversion von Matrizen,? Wiss. Z.Tech. Hochsch. Karl Marx Stadt,8, Nos. 4?5, 259?273 (1966). · Zbl 0196.47803
[635] W. Dück, ?Inversion symmetrischer Matrizen durch Abanderungsmethoden,? Z. Angew. Math. Mech.,46, Sonderh., T41-T43 (1966).
[636] W. Dück, ?Abänderung der Koeffizientenmatrix linearer Gleichungssysteme,? Math. Wirtschaft,4, 130?157 (1967).
[637] I. S. Duff, ?On a factored form of the inverse for sparse matrices,? D. Phil. Thesis, Oxford Univ. (1972).
[638] I. S. Duff, ?On the number of nonzeros added when Gaussian elimination is performed on sparse random matrices,? Math. Comput.,28, No. 125, 219?230 (1974). · Zbl 0298.65024 · doi:10.1090/S0025-5718-1974-0331756-7
[639] I. S. Duff and J. K. Reid, ?A comparison of sparsity orderings for obtaining a pivotal sequence in Gaussian elimination,? J. Inst. Math. Appl.,14, No. 3, 281?291 (1974). · Zbl 0308.65021 · doi:10.1093/imamat/14.3.281
[640] R. J. Duffin, ?A minimax theory for overdamped networks,? J. Rat. Mech. Anal.,4, No. 2, 221?233 (1955). · Zbl 0068.20904
[641] R. J. Duffin, ?The Rayleigh-Ritz method for dissipative or gyroscopic systems,? Q. Appl. Math.,18, 215?221 (1960). · Zbl 0102.39103 · doi:10.1090/qam/122048
[642] H. M. Dufour, ?Resolution des systemes lineaires par la methode des residus conjugues,? Rev. Franc. Traitement Inform. Chiffres,7, No. 2, 125?134 (1964).
[643] H. M. Dufour, ?Resolution des systemes lineaires par la methode des residus conjugues,? Bull. Geod., No. 71, 65?87 (1964). · doi:10.1007/BF02526082
[644] A. L. Dulmage and N. S. Mendelsohn, ?On the inversion of sparse matrices,? Math. Comput.,16, No. 80, 494?496 (1962). · Zbl 0115.11301 · doi:10.1090/S0025-5718-1962-0156452-2
[645] J. F. Durand, ?L’algorithme de Gauss-Seidel applique a un probleme unilateral non symetrique,? Rev. Franc. Inform, et Rech. Oper.,6, No. R-2, 23?30 (1972).
[646] C. S. Duris, ?An exchange method for solving Haar or non Haar overdetermined linear equations in the sense of Chebyshev,? Proc. 23rd ACM Nat. Conf., Princeton, New Jersey, 1968, London, 61?66 (1968).
[647] C. S. Duris and V. P. Sreedharan, ?Chebyshev and L1 solutions of linear equations using least squares solutions,? SIAM J. Numer. Anal.,5, No. 3, 491?505 (1968). · Zbl 0174.46901 · doi:10.1137/0705040
[648] C. S. Duris and M. G. Temple, ?A finite step algorithm for determining the ?strict? Chebyshev solution to Ax=b,? SIAM J. Numer. Anal.,10, No. 4, 690?699 (1973). · Zbl 0232.65033 · doi:10.1137/0710060
[649] P. S. Dwyer, ?Matrix inversion with the square root method,? Technometrics,6, 197?213 (1964). · Zbl 0122.12105 · doi:10.1080/00401706.1964.10490164
[650] M. C. Easton, ?A fixed method for Tchebycheff solution of inconsistent linear equations,? J. Inst. Math. Appl.,12, No. 2, 137?154 (1973). · Zbl 0276.90035 · doi:10.1093/imamat/12.2.137
[651] P. J. Eberlein, ?A two parameter test matrix,? Math. Comput.,18, No. 86, 296?298 (1964). · doi:10.1090/S0025-5718-1964-0170462-2
[652] P. J. Eberlein, ?On the convergence of some algorithms for the diagonalization and triangularization of matrices. Linear algebraic systems,? Proc. IFIP Congr. 65, New York City, 1965, Spartan Books, Washington, McMillan, London (1966), pp. 421?422.
[653] P. J. Eberlein, ?Solution to the complex eigenproblem by a norm reducing Jacobi type method,? Numer. Math.,14, No. 3, 232?245 (1970). · Zbl 0194.46803 · doi:10.1007/BF02163332
[654] P. J. Eberlein, ?On the diagonalization of complex symmetric matrices,? J. Inst. Math. Appl.,7, No. 3, 377?383 (1971). · Zbl 0221.65068 · doi:10.1093/imamat/7.3.377
[655] P. J. Eberlein and J. Boothroyd, ?Solution to the eigenproblem by a norm reducing Jacobi type method,? Numer. Math.,11, No. 1, 1?12 (1968). · Zbl 0157.22605 · doi:10.1007/BF02165467
[656] D. J. Edelbute, ?Matrix inversion by rank annihilation,? Math. Comput.,20, No. 93, 149?151 (1966). · doi:10.1090/S0025-5718-1966-0189227-2
[657] H. Edelmann, ?Ordered triangular factorization of matrices,? Proc. Power Systems Comput. Conf., London (1963).
[658] H. Edelmann, ?Optimale Strategien bei der direkten Auflösung linearer Gleichungssysteme mit schwachbesetzten Matrizen,? Z. Angew. Math. Mech.,45, Sonderh., T13-T18 (1965). · Zbl 0196.47902 · doi:10.1002/zamm.19650450413
[659] H. Edelmann, ?Massnahmen zur Reduction des Rechenaufwands bei der Berechnung grosser electrischer Netze,? Elektron. Rechenanlagen,10, 118?123 (1968).
[660] L. W. Ehrlich, ?The block symmetric successive overrelaxation method,? SIAM J. Appl. Math.,12, No. 4, 807?826 (1964). · Zbl 0133.38004 · doi:10.1137/0112068
[661] L. W. Ehrlich, ?Complex matrix inversion versus real,? Commun. ACM,13, No. 9, 561?562 (1970). · Zbl 0212.16905 · doi:10.1145/362736.362751
[662] M. P. Ekstrom, ?An iterative-improvement approach to the numerical solution of vector Toeplitz systems,? in: 5th Asilomar Conf. Circuits and Syst., Pacific Grove, Calif., Conf. Rec, North Hollywood, Calif. (1972), pp. 71?78.
[663] M. P. Ekstrom, ?An iterative-improvement approach to the numerical solution of vector Toeplitz systems,? IEEE Trans. Comput.,C-23, No. 3, 320?325 (1974). · Zbl 0289.65015 · doi:10.1109/T-C.1974.223929
[664] M. Engeli, T. Ginsburg, H. Rutishauser, and E. Stiefel, ?Refined iterative methods for computation of the solution and the eigenvalues of self-adjoint boundary value problems,? Mitt. Inst. Angew. Math. Zurich, No. 8 (1959). · Zbl 0089.12103
[665] Th. S. Englar, ?More test matrices for determinants and inverses,? Commun. ACM,6, No. 12, 745 (1963). · doi:10.1145/763973.763981
[666] I. Erdelyi, ?An iterative least-square algorithm suitable for computing partial eigensystems,? SIAM J. Minier. Anal.,2, No. 3, 421?436 (1965). · Zbl 0171.36005
[667] I. Erdelyi, ?On speeding convergence of an iterative eigenvalue process,? Comput. J.,8, No. 2, 159?165 (1965). · Zbl 0251.65029 · doi:10.1093/comjnl/8.2.159
[668] I. Erdelyi, ?On the ?reverse order law? related to the generalized inverse of matrix products,? J. Assoc. Comput. Mach.,13, No. 3, 439?443 (1966). · Zbl 0166.03103 · doi:10.1145/321341.321353
[669] A. M. Erisman and J. K. Reid, ?Monitoring the stability of the triangular factorization of a sparse matrix,? Numer. Math.,22, No. 3, 183?186 (1974). · Zbl 0271.65021 · doi:10.1007/BF01436966
[670] D. J. Evans, ?Estimation of the line overrelaxation factor and convergence rates of an alternating direction line overrelaxation technique,? Comput. J.,7, No. 4, 318?321 (1965). · Zbl 0138.09703 · doi:10.1093/comjnl/7.4.318
[671] D. J. Evans, ?The use of preconditioning in iterative methods for solving linear equations with symmetric positive-definite matrices,? J. Inst. Math. Appl.,4, No. 3, 295?314 (1968). · Zbl 0232.65031 · doi:10.1093/imamat/4.3.295
[672] D. J. Evans, ?An algorithm for the solution of certain tridiagonal systems of linear equations,? Comput. J.,15, No. 4, 356?359 (1972). · Zbl 0249.65017 · doi:10.1093/comjnl/15.4.356
[673] D. J. Evans, ?A new iterative procedure for the solution of sparse systems of linear difference equations,? in: Sparse Matrices and Applications, Plenum Press, New York-London (1972), pp. 89?100.
[674] D. J. Evans and C. V. D. Forrington, ?Note on the solution of certain tridiagonal systems of linear equations,? Comput. J.,5, No. 4, 327?328 (1963). · Zbl 0115.34401 · doi:10.1093/comjnl/5.4.327
[675] D. J. Evans and C. V. D. Forrington, ?An iterative process for optimizing symmetric successive overrelaxation,? Comput. J.,6, No. 3, 271?273 (1963). · Zbl 0127.08202 · doi:10.1093/comjnl/6.3.271
[676] P. Facq, ?Sur l’inversion d’une matrice de Toeplitz par blocs,? C. R. Acad. Sci.,A278, No. 26, 1645?1648 (1974). · Zbl 0289.65014
[677] D. K. Faddeev, V. H. Kublanovskaya, and V. H. Faddeeva, ?Sur les systemes lineaires algebriques de matrices rectangulaires et mal-conditionnees,? Colloq. Internat. Centre Nat. Rech. Scient., No. 165, 161?172 (1968).
[678] D. K. Faddeev and V. N. Faddeeva, ?Stability in linear algebra problems,? Proc. IFIP Congr. 68, Edinburgh, 9168, Vol. 1: Mathematics, Software, North-Holland, Amsterdam (1969), pp. 33?39. · Zbl 0195.44805
[679] D. F. Faddeev and V. N. Faddeeva, ?Natural norms in algebraic processes,? SIAM J. Numer. Anal.,7, No. 4, 520?531 (1970). · Zbl 0222.65055 · doi:10.1137/0707042
[680] A. Fadini, ?Beitrag zur Lösung eines inversen Eigenwertproblems,? Z. Angew. Math. Mech.,44, Nos. 10/11, 506?508 (1964). · Zbl 0131.34003 · doi:10.1002/zamm.19640441012
[681] A. Fadini, ?Molekülkraftkonstantenberechnung als inverses Eigenwertproblem,? Z. Angew. Math. Mech.,45, Sonderh., T29-T31 (1965).
[682] A. Fadini, ?Einige Anwendungen eines erweiterten inversen Eigenwertproblems,? Z. Angew. Math. Mech.,46, Sonderh., T52-T54 (1966).
[683] S. Falk, ?Klassifikation gedämpfter Schwingungssysteme und Eingrenzung ihrer Eigenwerte,? Ing. Arch.,29, No. 6, 436?444 (1960). · Zbl 0095.38601 · doi:10.1007/BF00536608
[684] S. Falk, ?Einschliessungssätze für Eigenwerte und-Vektoren normaler Matrizenpaare,? Wiss. Z. Tech. Univ. Dresden,10, No. 5, 1033?1039 (1961).
[685] S. Falk, ?Eine Variante zur Gauss -Seideischen Iteration linearer Gleichungssysteme,? Elektron. Datenverarb.,5, No. 5, 230?234 (1963).
[686] S. Falk, ?Einschliessungssätze für die Eigenwerte normaler Matrizenpaare,? Z. Angew. Math. Mech.,44, Nos. 1?2, 41?55 (1964). · Zbl 0163.38804 · doi:10.1002/zamm.19640440104
[687] S. Falk, ?Einschliessungssätze für die Eigenvektoren normaler Matrizenpaare,? Z. Angew. Math. Mech.,45, No. 1, 47?56 (1965). · Zbl 0163.38901 · doi:10.1002/zamm.19650450107
[688] S. Falk, ?über die Eigenwerte benachbarter normaler Matrizenpaare,? Z. Angew. Math. Mech.,5, Nos. 6?7, 431?433 (1970). · Zbl 0207.15701 · doi:10.1002/zamm.19700500619
[689] S. Falk, ?Ein einfaches Iterationsverfahren zur Bestimmung der Eigenwerte eines Hermitesehen (reellsymmetrischen) Matrizenpaares,? Acta Tech. Acad. Sci. Hung.,73, Nos. 3?4, 327?334 (1972). · Zbl 0307.65044
[690] S. Falk, ?Berechnung von Eigenwerten und Eigenvektoren normaler Matrizenpaare durch Ritz-Iteration,? Z. Angew. Math. Mech.,53, No. 2, 73?91 (1973). · Zbl 0256.65023 · doi:10.1002/zamm.19730530202
[691] Ky Fan and A. J. Hoffman, ?Some metric inequalities in the space of matrices,? Proc. Am. Math. Soc.,3, No. 1, 111?116 (1955). · Zbl 0064.01402 · doi:10.1090/S0002-9939-1955-0067841-7
[692] F. Fazekas, ?Matrix algorithms for tasks connected with symmetrical matrices,? Z. Angew. Math. Mech.,53, No. 4, T186-T188 (1973). · Zbl 0277.65020
[693] D. Feingold and D. Spohn, ?Un theoreme simple sur les normes de matrices et ses consequences,? C. R. Acad. Sci.,256, No. 13, 2758?2760 (1963). · Zbl 0107.10502
[694] H. Feldmann, ?Eine einfache Strategie für eine Klasse linearer Iterationsverfahren und nichtlineare Konvergenzbeschleunigung,? Z. Angew. Math. Mech.,48, No. 8, Sonderh., T61-T65 (1969).
[695] M. G. Feier, ?Calculation of eigenvectors of large matrices,? J. Comput. Phys.,14, No. 4, 341?349 (1974). · Zbl 0285.65026 · doi:10.1016/0021-9991(74)90017-5
[696] T. I. Fenner and G. Loizou, ?Matrix bounds on the spectral condition number,? Linear Algebra Appl.,8, 157?178 (1974). · Zbl 0282.15004 · doi:10.1016/0024-3795(74)90053-6
[697] T. I. Fenner and G. Loizou, ?Some new bounds on the condition numbers of optimally scaled matrices,? J. Assoc. Comput. Mach.,21, No. 3, 514?524 (1974). · Zbl 0298.65030 · doi:10.1145/321832.321849
[698] H. E. Fettis, ?Note on the matrix equation Ax=?Bx,? Comput. J.,8, No. 3, 279 (1965). · Zbl 0135.37601 · doi:10.1093/comjnl/8.3.279
[699] H. E. Fettis and J. C. Caslin, ?Eigenvalues and eigenvectors of Hilbert matrices of order 3 through 10,? Math. Comput.,21, No. 99, 431?441 (1967). · Zbl 0153.18004
[700] M. Fiedler, ?On inverting partitioned matrices,? Chekh. Mat. Zh.,88, No. 4, 574?586 (1963). · Zbl 0121.26104
[701] M. Fiedler, ?Some remarks on numerical solution of linear problems,? Apl. Mat.,10, No. 2, 190?193 (1965).
[702] M. Fiedler and V. Ptak, ?On matrices with nonpositive off-diagonal elements and positive principal minors,? Chekh. Mat. Zh.,12, 382?400 (1962). · Zbl 0131.24806
[703] M. Fiedler and V. Patk, ?Generalized norms of matrices and the location of the spectrum,? Chekh. Mat. Zh.,12, No. 4, 558?571 (1962).
[704] M. Fiedler and V. Ptak, ?Sur la meilleure approximation des transformations lineaires par des transformations de rang prescrit,? C. R. Acad. Sci.,254, No. 22, 3805?3807 (1962). · Zbl 0108.01401
[705] M. Fiedler and V. Ptak, ?On aggregation in matrix theory and its application to numerical inverting of large matrices,? Bull. Acad. Pol. Sci. Ser. Mat., Astron. Phys.,11, No. 12, 757?759 (1963). · Zbl 0235.65027
[706] M. Fiedler and V. Ptak, ?Estimates and iteration procedures for proper values of almost decomposable matrices,? Chekh. Mat. Zh.,14, No. 4, 593?608 (1964). · Zbl 0243.65011
[707] M. Fiedler and V. Ptak, ?Some results on matrices of class K and their application to the convergence rate of iteration procedures,? Chekh. Mat. Zh.,16, No. 2, 260?273 (1966).
[708] G. Fischer and J. Roppert, ?Über ein Theorem von Eckart und Young: ?Eine Verallgemeinerung eines Transformationsverfahrens von Jacobi?,? Metrika,10, 161?170 (1966). · Zbl 0145.40201 · doi:10.1007/BF02613428
[709] H. Fischer, ?Intervall-Arithmetiken für komplexe Zahlen,? Z. Angew. Math. Mech.,53, No. 4, 190?191 (1973). · Zbl 0262.65032
[710] K. E. Fitzgerald, ?Error estimates for the solution of linear algebraic systems,? J. Res. Nat. Bur. Stand.,B74, No. 4, 251?310 (1970). · Zbl 0225.65045 · doi:10.6028/jres.074B.024
[711] K. E. Fitzgerald, ?Comparison of some FORTRAN programs for matrix inversion,? J. Res. Nat. Bur. Stand.,B78, No. 1, 15?33 (1974). · Zbl 0281.65024 · doi:10.6028/jres.078B.005
[712] G. Fix and R. Heiberger, ?An algorithm for the ill-conditioned generalized eigenvalue problem,? SIAM J. Numer. Anal.,9, No. 1, 78?88 (1972). · Zbl 0252.65028 · doi:10.1137/0709009
[713] R. Fletcher, ?A technique for orthogonalization,? J. Inst. Math. Appl.,5, No. 2, 162?166 (1969). · Zbl 0185.07703 · doi:10.1093/imamat/5.2.162
[714] K. Florek, ?Some remarks on solving systems of linear equations by a relaxation method combined with a generalized Hotelling method for inverting matrices,? Zast. Mat.,8, No. 4, 347?350 (1966). · Zbl 0142.11501
[715] J. Focke, ?Über die Kondition linearer Gleichungssysteme,? Wiss. Z. Karl-Marx-Uniw. Leipzig. Math.-Naturwiss. Reihe,11, No. 1, 41?43 (1962). · Zbl 0104.10002
[716] J. Focke, ?Eine Zusammenhang zwischen Konditionszahlen,? Z. Angew. Math. Mech.,53, No. 12, 805 (1973). · Zbl 0267.65032 · doi:10.1002/zamm.19730531113
[717] P. Forster, ?Bemerkungen zum Iterationsverfahren von Schulz zur Bestimmung der Inversen einer Matrix,? Numer. Math.,12, No. 3, 211?214 (1968). · Zbl 0165.50203 · doi:10.1007/BF02162913
[718] G. E. Forsythe, ?Today’s computational methods of linear algebra,? SIAM Rev.,9, No. 3, 489?515 (1967). · doi:10.1137/1009071
[719] G. E. Forsythe, ?On the asymptotic directions of the S-dimensional optimum gradient method,? Numer. Math.,11, No. 1, 57?76 (1968). · Zbl 0153.46004 · doi:10.1007/BF02165472
[720] G. E. Forsythe and R. A. Leibler, ?Correction to the article. ?Matrix inversion by a Monte-Carlo process?,? Math. Tables and Other Aids Comput.,5, No. 33, 55 (1951). · doi:10.2307/2002293
[721] G. E. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, Englewood Cliffs, New Jersey (1967), Chap. IX. · Zbl 0154.40401
[722] G. E. Forsythe and J. Ortega, ?Attempts to determine the optimum factor for successive overrelaxation,? Proc. Int. Conf. Inform. Process., Unveco, Paris, 110 (1960).
[723] A. J. Fox and F. A. Johnson, ?On finding the eigenvalues of real symmetric tridiagonal matrices,? Comput. J.,9, No. 1, 98?105 (1966). · Zbl 0142.11605 · doi:10.1093/comjnl/9.1.98
[724] B. L. Fox, ?Reducing the number of multiplications in iterative processes,? Acta. Inf.,3, No. 1, 43?45 (1973). · Zbl 0261.65029 · doi:10.1007/BF00288651
[725] B. L. Fox, An Introduction to Numerical Linear Algebra, Clarendon Press, Oxford (1964), Chap. XI. · Zbl 0122.35701
[726] P. Franck, ?Sur la meilleure approximation d’une matrice donnee par une matrice singuliere,? C. R. Acad. Sci.,253, No. 13, 1297?1298 (1961).
[727] P. Franck, ?Sur la distance minimale d’une matrice reguliere donnee au lieu des matrices singulieres,? 2-e Congr. Assoc. Franc. Calcul. et Traitem. Inform., AFCALTI, Paris, 1961, Paris, 55?60 (1962).
[728] P. Franck, ?Sur la plus courte distance d’une matrice donnee a l’ensemble des matrices singulieres,? C. R. Acad. Sci.,256, No. 18, 3799?3801 (1963). · Zbl 0196.29901
[729] J. N. Franklin, ?Well-posed stochastic extensions of ill-posed linear problems,? J. Math. Anal. Appl.,31, No. 3, 682?716 (1970). · Zbl 0198.20601 · doi:10.1016/0022-247X(70)90017-X
[730] R. Franzen, ?Die intervallanalytische Behandlung parameterabhängiger Gleichungssysteme,? Ber. Ges. Math. Datenverarb., No. 47, 63 (1971). · Zbl 0276.65026
[731] M. Fraser and N. Metropolis, ?Algorithms in unnormalized arithmetic. III. Matrix inversion,? Numer. Math.,12, No. 5, 416?428 (1968). · Zbl 0184.37503 · doi:10.1007/BF02161364
[732] T. Frey, ?Einige neue Methoden zur numerischen Berechnung von Eigenwerten,? Apl. Mat.,10, No. 3, 206?212 (1965).
[733] T. Frey, ?Über die Lösung einiger numerisch instabiter Probleme der linearen Algebra,? Wiss. Z. Tech. Univ. Dresden,17, No. 5, 1134 (1968).
[734] I. Freid, ?More on gradient iterative methods in finite-element analysis,? AIAA J.,7, No. 3, 565?567 (1969). · Zbl 0185.52602 · doi:10.2514/3.5166
[735] I. Freid, ?Optimal gradient minimization scheme for finite element eigenproblems,? J. Sound Vibr.,20, No. 3, 333?342 (1972). · Zbl 0242.65041 · doi:10.1016/0022-460X(72)90614-1
[736] C. -E. Fröberg, ?On triangularization of complex matrices by two-dimensional unitary transformations,? BIT,5, No. 4, 230?234 (1965). · Zbl 0244.65026 · doi:10.1007/BF01937502
[737] C.-E. Fröberg, Introduction to Numerical Analysis, Adiwes Int. Ser., Addison-Wesley, Reading, Mass., London (1965).
[738] M. Fröhner, ?Stabilitätsuntersuchung eines verallgemeinerten Iterationsprozesses zur Lösung linearer Gleichungssysteme,? Beitr. Numerisch. Math., Berlin, 19?23 (1974). · Zbl 0294.65023
[739] D. R. Fulkerson and P. Wolfe, ?An algorithm for scaling matrices,? SIAM Rev.,4, No. 2, 42?146 (1962). · Zbl 0108.12401 · doi:10.1137/1004032
[740] V. Gabriel and I. Serdült, ?Generalizarea metodei lui Schulz pentru calculul inversei unei matrici,? Stud. Si Cerc. Mat.,20, No. 7, 969?979 (1968).
[741] J. Gaches, ?Compatibilite d’une solution xavecunsysteme lineaire donne,? C. R. Acad. Sci.,262, No. 6, A348-A349 (1966). · Zbl 0137.32805
[742] J. Gaches, ?Compatibilite d’une solution calculee avec les donnees d’un systeme lineaire,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 135?140 (1968).
[743] J. Gaches, J.-L. Rigal, and X. Rousset de Pina, ?Distance euclidienne d’une application lineaire ? au lieu des applications de rang r donne. Determination d’une meilleure approximation de rangr,? C. R. Acad. Sci.,260, No. 22, A5672-A5674 (1965). · Zbl 0133.38103
[744] D. Gaier and J. Todd, ?On the rate of convergence of optimal ADI processes,? Numer. Math.,9, No. 5, 452?459 (1967). · Zbl 0154.41101 · doi:10.1007/BF02162159
[745] L. Garcia de Viedma, ?Sistemas de ecuaciones lineales,? Estruduras,4, Nos. 7?8, 53?64 (1965).
[746] L. Garcia de Viedma and V. J. Torres, ?Metodo iterativo para el calculo de la inversa de una matriz, partiendo de una aproximacion dada,? Publ. Grupo Alanisis Numerico Dep. Calculo, Matrid, 7?10 (1965).
[747] G. O. Gardner, Numerical Error in Iterative Processes, Div. Appl. Math., Brown Univ., Providence, R. I. (1965).
[748] I. Gargantini, ?On the computation of the eigenvalues of a tridiagonal matrix,? Math. Comput.,23, No. 106, 403?405 (1969). · Zbl 0182.21402 · doi:10.1090/S0025-5718-1969-0242359-5
[749] M. Garnett, A. Ben-Israel, and S. Yau, ?A hyperpower iterative method for computing matrix products involving the generalized inverse,? SIAM J. Numer. Anal.,8, No. 1, 104?109 (1971). · Zbl 0217.52605 · doi:10.1137/0708013
[750] J. Gary, ?Hyman’s method applied to the general eigenvalue problem,? Math. Comput.,19, No. 90, 314?316 (1965). · Zbl 0129.09603
[751] J. Gary, ?On convergence rates for line over relaxation,? Math. Comput.,21, No. 98, 220?223 (1967). · doi:10.1090/S0025-5718-1967-0223111-1
[752] Cl. Gasquet, ?Une borne d’erreur dans la resolution de problemes lineaires perturbes et regularises,? Rev. Frac. Inform. et Rech. Oper.,5, No. R-3, 96?100 (1971).
[753] N. Gastinel, ?Inversion d’une matrice generalisant la matrice de Hubert,? Rev. Franc. Traitement Inform. Chiffres,3, 149?152 (1960).
[754] N. Gastinel, ?Utilisation de matrices verifiant une equation de degre 2 pour la transmutation de matrices,? C. R. Acad. Soi.,250, No. 11, 1960?1961 (1960).
[755] N. Gastinel, ?Matrices du second degre et normes generales en analyse numerique lineaire,? These, Doct. Sci. Math. Fac. Sci. Univ. Grenoble (1960).
[756] N. Gastinel, ?Quelques procedes iteratifs pour la resolution de systemes lineaires associes, par la methode des differences a des equations aux derivees partielles,? 2-e Congr. Assoc. Franc. Calcul et Traitem. Inform. AFCALTI, Paris, 1961, Paris, 39?46 (1962).
[757] N. Gastinel, ?Sur le meilleur choix des parametres de sur-relaxation,? Rev. Franc. Traitement Inform. Chiffres,5, No. 2, 109?126 (1962).
[758] N. Gastinel, ?Sur-decomposition de normes generales et procedes iteratifs,? Numer. Math.,5, No. 2, 142?151 (1963). · Zbl 0114.32201 · doi:10.1007/BF01385886
[759] N. Gastinel, ?Quelques problemes recents relatifs aux normes de vecteurs et de matrices,? 4-e Congr. Calcul et Traitem. Inform. AFIRO, Versailles, 1964, Paris, 193?199 (1965).
[760] N. Gastinel, ?Proprietes de certains ensembles normes de matrices,? Numer. Math.,7, No. 3, 255?260 (1965). · Zbl 0168.03103 · doi:10.1007/BF01436082
[761] N. Gastinel, Analyse Numerique Lineaire, Hermann, Paris (1966), Chap. XII.
[762] N. Gastinel, ?Conditionnement des problemes d’approximation (aux moindres carres) et des problemes de lissage,? Colloq. Internat. Centre Nat. Rech. Scient., No. 165, 111?118 (1968).
[763] N. Gastinel, ?Sur l’extension de normes sur des algebres de matrices,? Numer. Math.,17, No. 1, 71?83 (1971). · Zbl 0245.15013 · doi:10.1007/BF01395868
[764] N. Gastinel, ?Sur le calcul des produits de matrices,? Numer. Math.,17, No. 3, 222?229 (1971). · Zbl 0227.65030 · doi:10.1007/BF01436378
[765] C. W. Gear, ?A simple set of test matrices for eigenvalue programs,? Math. Comput.,23, No. 105, 119?125 (1969). · doi:10.1090/S0025-5718-1969-0238477-8
[766] R. Geets, ?Conditiegetallen voor de inversie van een matrix,? Rev. X, No. 1, 35?51 (1970).
[767] E. Gekeler, ?Ein optimales zweistufiges Interationsverfahren,? Z. Angew. Math. Mech.,53, No. 4, T192-T193 (1973). · Zbl 0259.65041
[768] B. Gellai, ?On hypermatrices with blocks commutable in pairs in the theory of molecular vibrations,? Stud. Sci. Math. Hung.,6, Nos. 3?4, 347?353 (1971).
[769] W. M. Gentleman, ?Least squares computation by Givens transformations without square roots,? J. Inst. Math. Appl.,12, No. 3, 329?336 (1973). · Zbl 0289.65020 · doi:10.1093/imamat/12.3.329
[770] A. George, ?A survey of sparse matrix methods in the direct solution of finite element equations,? Proc. Summer Comput. Simul. Conf., Montreal, 1973, Vol. 1, La Jolla, Calif. (1973), pp. 15?20.
[771] A. George, ?On block elimination for sparse linear systems,? SIAM J. Numer. Anal.,11, No. 3, 585?603 (1974). · Zbl 0253.65014 · doi:10.1137/0711050
[772] J. Gergely, ?Ritka matrixok invertalasa,? Közl., MTA Szamitastechn. es Automatiz. Kut. Intez., No. 11, 51?54 (1973).
[773] B. Germain-Bonne, ?Calcul de pseudoinverses,? Rev. Franc. Inf. Rech. Oper.,8, No. R-2, 3?13 (1969). · Zbl 0193.11803
[774] J. C. Geuder, Error Analysis of a Direct Method of Solution of Simultaneous Linear Equation Systems, Div. Appl. Math., Brown Univ., Providence, Rhode Island (1965).
[775] N. E. Gibbs and W. G. Poole, ?Tridiagonalization by permutations,? Commun. ACM,17, No. 1, 20?24 (1974). · Zbl 0271.65024 · doi:10.1145/360767.360783
[776] P. E. Gill, G. H. Golub, W. Murray, and M. A. Saunders, ?Methods for modifying matrix factorization,? Math. Comput.,28, No. 126, 505?535 (1974). · Zbl 0289.65021 · doi:10.1090/S0025-5718-1974-0343558-6
[777] A. W. Gillies, ?On the classification of matrix generalized inverses,? SIAM Rev.,12, No. 4, 573?576 (1970). · Zbl 0205.33003 · doi:10.1137/1012107
[778] T. Ginsburg, ?The conjugate gradient method,? Numer. Math.,5, No. 2, 191?200 (1963). · Zbl 0123.11201 · doi:10.1007/BF01385890
[779] T. Ginsburg, ?The conjugate gradient method,? Grundlehren Math. Wiss. Einzeldarstell.,186, 57?69 (1971).
[780] G. H. Glaser, Automatic Bandwidth Reduction Techniques, Rep. 72-260, DBA Systems, Inc., Florida, Melbourne (1972).
[781] D. Goldfarb, ?Modification methods for inverting matrices and solving systems of linear algebraic equations,? Math. Comput.,26, No. 120, 829?852 (1972). · Zbl 0268.65026 · doi:10.1090/S0025-5718-1972-0317527-4
[782] A. A. Goldstein and W. Cheney, ?A finite algorithm for the solution of consistent linear equations and inequalities and for the Tchebycheff approximation of inconsistent linear equations,? Pac. J. Math.,8, No. 3, 415?427 (1958). · Zbl 0084.01902 · doi:10.2140/pjm.1958.8.415
[783] M. J. Goldstein, ?Reduction of the eigenproblem for Hermitian persymmetric matrices,? Math. Comput.,28, No. 125, 237?238 (1974). · Zbl 0279.65033 · doi:10.1090/S0025-5718-1974-0329226-5
[784] G. H. Golub, ?The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared with the method of successive overrelaxation,? Doct. Thesis, Univ. of Illinois (1959).
[785] G. H. Golub, ?Bounds for the round-off errors in the Richardson second-order method,? BIT,2, 212?223 (1962). · Zbl 0107.33304 · doi:10.1007/BF01940168
[786] G. H. Golub, ?Bounds for eigenvalues of tridiagonal symmetric matrices computed by the LR method,? Math. Comput.,16, No. 80, 438?445 (1962). · Zbl 0107.33402 · doi:10.1090/S0025-5718-1962-0163430-6
[787] G. H. Golub, ?Bounds for the round-off errors in the Richardson second-order method,? Proc. IFIP Congr. 62, Munich, 1962, North-Holland, Amsterdam (1963), pp. 207?208. · Zbl 0107.33304
[788] G. H. Golub, ?Numerical methods for solving linear least squares problems,? Numer. Math.,7, No. 3, 206?216 (1965). · Zbl 0142.11502 · doi:10.1007/BF01436075
[789] G. H. Golub, ?Numerical methods for solving linear least squares problems,? Apl. Mat.,10, No. 3, 213?216 (1965). · Zbl 0142.11502
[790] G. H. Golub, ?Least squares, singular values, and matrix approximations,? Apl. Mat.,13, No. 1, 44?51 (1968). · Zbl 0179.21403
[791] G. H. Golub, ?Some modified matrix eigenvalue problems,? SIAM Rev.,15, No. 2, Part 1, 318?334 (1973). · Zbl 0254.65027 · doi:10.1137/1015032
[792] G. H. Golub, ?Some uses of the Lanczos algorithm in numerical linear algebra,? in: Top. Numer. Anal., London-New York (1973), pp. 173?184.
[793] G. H. Golub and W. Kahan, ?Calculating the singular values and pseudoinverse of a matrix,? SIAM J. Numer. Anal.,2, No. 2, 205?224 (1965). · Zbl 0194.18201
[794] G. H. Golub and C. Reinsch, ?Singular value decomposition and least squares solutions,? Numer. Math.,14, No. 5, 403?420 (1970). · Zbl 0181.17602 · doi:10.1007/BF02163027
[795] G. H. Golub, R. Underwood, and J. H. Wilkinson, ?The Lanczos algorithm for the symmetric Ax=?Bx problem,? Stanford Univ., Stan-CS-72-270 (1972).
[796] G. H. Golub and J. M. Varah, ?On a characterization of the best l(in2) scaling of a matrix,? SIAM J. Numer. Anal.,11, No. 3, 472?479 (1974). · Zbl 0314.65019 · doi:10.1137/0711039
[797] G. H. Golub and J. H. Wilkinson, ?Note on the iterative refinement of least squares solution,? Numer. Math.,9, No. 2, 139?148 (1966). · Zbl 0156.16106 · doi:10.1007/BF02166032
[798] A. Goraj, M. Jankowski, A. Kielbasinski, and H. Wozniakowski, ?Oszacowanie bledu rozwiazania ukladu rownan linowych i zastosowanie poprawianego sumowania w algorytmach algebry liniowej,? Rocz. Pol. Tow. Math., Ser. 3,1, 43?46 (1973).
[799] A. R. Gourlay, ?The acceleration of the Peaceman-Rachford method by Chebyshev polynomials,? Comput. J.,10, No. 4, 378?382 (1968). · Zbl 0155.19902 · doi:10.1093/comjnl/10.4.378
[800] A. R. Gourlay, ?On Chebychev acceleration procedures for alternating direction iterative methods,? J. Inst. Math. Appl.,6, No. 1, 1?11 (1970). · Zbl 0188.22002 · doi:10.1093/imamat/6.1.1
[801] A. R. Gourlay and G. A. Watson, Computational Methods for Matrix Eigenproblems, Wiley, London (1973), Chap. X1 · Zbl 0264.65030
[802] J. Grad, ?Matrix balancing,? Comput. J.,14, No. 3, 280?284 (1971). · Zbl 0226.65030 · doi:10.1093/comjnl/14.3.280
[803] J. Grad, K. A. Redish, and M. A. Brebner, ?Calculation of eigenvalues of real matrices by the QR method using double QR step. Algorithm 32,? Comput. J.,11, No. 1, 112?114 (1968). · doi:10.1093/comjnl/11.1.112
[804] J. Grad and E. Zakrajsek, ?LR algorithm with Laguerre shift for symmetric tridiagonal matrices,? Comput. J.,15, No. 3, 268?270 (1972). · Zbl 0243.65010 · doi:10.1093/comjnl/15.3.268
[805] D. J. Green, ?The simple iterative method applied to a matrix which has a dominant double real eigenvalue,? Math. Gaz.,49, No. 368, 179?184 (1965). · Zbl 0132.25307 · doi:10.2307/3612312
[806] R. T. Gregory and D. L. Karney, A Collection of Matrices for Testing Computational Algorithms, Wiley, New York-London (1969), Chap. DC. · Zbl 0195.44803
[807] P. M. Gresho and R. L. Sani, ?Direct method for inverting symmetric tridiagonal and quasitridiagonal matrices,? Trans. ASME,E37, No. 4, 1194?1195 (1970). · doi:10.1115/1.3408695
[808] T. N. E. Greville, ?Note on the generalized inverse of a matrix product,? SIAM Rev.,8, No. 4, 518?521 (1966). · Zbl 0143.26303 · doi:10.1137/1008107
[809] T. N. E. Greville, ?Spectral generalized inverses of singular square matrices,? Notices Am. Math. Soc.,15, No. 1, 111 (1968).
[810] T. N. E. Greville, ?Some new generalized inverses with spectral properties,? Proc. Symp. on Theory and Appl. of Generalized Inverses of Matrices, Texas Tech. College, Lubbock, Texas (1968), pp. 26?46.
[811] T. N. E. Greville, ?Solution of the matrix equation XAX=X, and relations between oblique and orthogonal projectors,? SIAM J. Appl. Math.,26, No. 4, 828?832 (1974). · Zbl 0288.15018 · doi:10.1137/0126074
[812] D. Gries, ?Über einige Klassen von Normen,? Diss., Dokt. Naturwiss. Fak. Allgern. Wiss. Techn. Hochsch. München (1966).
[813] D. Gries, ?Characterizations of certain classes of norms,? Numer., Math.,10, No. 1, 30?41 (1967). · Zbl 0164.17603 · doi:10.1007/BF02165157
[814] D. Grossiord, ?Application de la methode de Laguerre au calcul des valeurs propres de matrices tridiagonales,? These. Doct. Math. Fac. Sci. Univ. Besancon (1966).
[815] D. Grossiord, ?Sur un algorithme de Laguerre utilisant la notion de saut,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 201?204 (1968). · Zbl 0207.15801
[816] K. G. Guderley, ?On nonlinear eigenvalue problems for matrices,? SIAM J. Appl. Math.,6, No. 4, 335?353 (1958). · Zbl 0085.33304 · doi:10.1137/0106024
[817] R. Guedj, ?L’utilisation d’inverses generalises dans la resolution de systemes lineaires de rang quelconque,? 3-e Congr. Calcul et Traitem. Inform. AFCALTI, Toulouse, 1963, Paris (1965), pp. 137?143.
[818] R. Guenther, ?A transform method for solving certain systems of linear algebraic equations,? Computing,8, Nos. 1?2, 13?18 (1971). · Zbl 0242.65037 · doi:10.1007/BF02234039
[819] W. H. Guilinger, ?The Peaceman-Rachford method for small mesh increments,? J. Math. Anal. Appl.,11, Nos. 1?3, 261?277 (1965). · Zbl 0133.38701 · doi:10.1016/0022-247X(65)90086-7
[820] W. H. Guilinger, ?The Peaceman-Rachford method for small mesh increments. Linear algebraic systems,? Proc. IFIP Congr. 65, New York City, 1965, Vol. 2, Spartan Books, Washington, MacMillan, London (1966). · Zbl 0133.38701
[821] J. Guittet, ?Une remarque sur les normes de matrices; application aux methodes de directions alternees a deux dimensions avec operateur de perturbation,? C. R. Acad. Sci.,257, No. 22, 3282?3285 (1963). · Zbl 0113.32103
[822] J. Guittet, ?Methodes de directions alternees a n dimensions avec operateur de perturbation,? C. R. Acad. Sci.,257, No. 23, 3557?3559 (1963). · Zbl 0113.32104
[823] J. Guittet, ?Méthodes de directions alternees,? Rev. Franc. Traitement Inf. Chiffres,9, No. 2, 95?107 (1966).
[824] J. Guittet, ?Une nouvelle methode de directions alternees a q variable,? J. Math. Anal. Appl.,17, 199?213 (1967). · Zbl 0146.13501 · doi:10.1016/0022-247X(67)90145-X
[825] K. K. Gupta, ?Solution of eigenvalue problems by Sturm sequence method,? Int. J. Numer. Meth. Eng.,4, No. 3, 379?404 (1972). · Zbl 0251.65028 · doi:10.1002/nme.1620040308
[826] K. K. Gupta, ?Eigenproblem solution by a combined Sturm sequence and inverse iteration technique,? Int. J. Numer. Meth. Eng.,7, No. 1, 17?42 (1973). · Zbl 0263.65044 · doi:10.1002/nme.1620070103
[827] K. K. Gupta, ?Author’s reply to a recent discussion: ?Solution of eigenvalue problems by Sturm sequence method?,? Int. J. Numer. Meth. Eng.,7, No. 4, 553?554 (1973). · doi:10.1002/nme.1620070413
[828] Haresh N. Gupta, ?An iterative method for computation of generalized inverse and matrix rank,? IEEE Trans. Syst., Man Cybern.,1, No. 1, 89?90 (1971). · Zbl 0226.65032 · doi:10.1109/TSMC.1971.5408613
[829] Naresh N. Gupta, ?On the convergence of an iterative method for the computation of generalized inverse and associated projections,? Int. J. Syst. Sci.,2, No. 1, 67?75 (1971). · Zbl 0241.65039 · doi:10.1080/00207727108920178
[830] Naresh N. Gupta, ?An optimum hyperpower iterative method for computing generalized inverses and associated projections,? Int. J. Syst. Sci.,4, No. 1, 1?3 (1973). · Zbl 0258.65044 · doi:10.1080/00207727308919989
[831] F. G. Gustavson, ?Some basic techniques for solving sparse systems of linear equations,? in: Sparse Matrices and Applications, Plenum Press, New York-London (1972), pp. 41?52.
[832] F. G. Gustavson, W. Liniger, and R. Willoughby, ?Symbolic generation of an optimal Crout algorithm for sparse systems of linear equations,? J. Assoc. Comput. Mach.,17, No. 1, 87?109 (1970). · Zbl 0187.09703 · doi:10.1145/321556.321565
[833] J. L. Guyot, ?Etude de quelques methodes de calcul du polynome caracteristique et des valeurs propres,? These Doct. Math. Appl. Fac. Sci. Univ. Grenoble (1969).
[834] K. P. Hadeler, ?Mehrparametrige und nichtlineare Eigenwetauf gaben,? Arch. Ration. Mech. Anal.,27, No. 4, 306?328 (1967). · Zbl 0166.41701 · doi:10.1007/BF00281717
[835] K. P. Hadeler, ?Inverse Eigenwertprobleme,? Z. Angew. Math. Mech.,47, Sonderh., T49-T50 (1967). · Zbl 0189.47804 · doi:10.1002/zamm.19670470204
[836] K. P. Hadeler, ?Ein inverses Eigenwertproblem,? Linear Algebra Appl.,1, No. 1, 83?101 (1968). · Zbl 0159.03602 · doi:10.1016/0024-3795(68)90051-7
[837] K. P. Hadeler, ?Newton-Verfahren für inverse Eigenwertaufgaben,? Numer. Math.,12, No. 1, 35?39 (1968). · Zbl 0167.45304 · doi:10.1007/BF02170994
[838] K. P. Hadeler, ?Variationsprinzipien bei nichtlinearen Eigenwertaufgaben,? Arch. Ration. Mech. Anal.,30, 297?307 (1968). · Zbl 0165.48101 · doi:10.1007/BF00281537
[839] K. P. Hadeler, ?Multiplikative inverse Eigenwertprobleme,? Linear Algebra Appl.,2, No. 1, 65?86 (1969). · Zbl 0182.05201 · doi:10.1016/0024-3795(69)90008-1
[840] K. P. Hadeler, ?Anwendung von Eixpunktsätzen auf nichtlineare Eigenwertaufgaben,? Math. Z.,112, No. 3, 181?189 (1969). · Zbl 0181.15102 · doi:10.1007/BF01110217
[841] K. P. Hadeler, ?Existenz- und Eindeutigkeitssätze für inverse Eigenwertaufgaben mit Hilfe des topologischen Abbildungsgrades,? Arch. Ration. Mech. Anal.,42, No. 4, 317?322 (1971). · Zbl 0223.15005 · doi:10.1007/BF00282335
[842] A. Hadjidimos, ?Extrapolated alternating direction implicit method for the numerical solution of elliptic partial differential equations,? Doct. Thesis, Univ. Liverpool (1968).
[843] A. Hadjidimos, ?Extrapolated alternating direction implicit iterative methods,? BIT,10, No. 4, 465?475 (1970). · Zbl 0252.65075 · doi:10.1007/BF01935566
[844] A. Hadjidimos, ?Optimum extrapolated alternating direction implicit schemes,? J. Inst. Math. Appl.,7, No. 3, 361?366 (1971). · Zbl 0235.65063 · doi:10.1093/imamat/7.3.361
[845] L. A. Hageman, ?Block iterative methods for two-cyclic matrix equations with special application to the numerical solution of the second-order self-adjoint elliptic partial differential equation in two dimensions,? Doct. Diss. Univ. Pittsburgh (1962).
[846] L. A. Hageman, ?The Chebyshev polynomial method of iteration,? Bettis Atomic Power Lab., Wapo-TM-537 (1967).
[847] L. A. Hageman and R. D. Kellogg, ?Estimating optimum overrelaxation parameters,? Math. Comput.,22, No. 101, 60?68 (1968). · Zbl 0165.50301 · doi:10.1090/S0025-5718-1968-0229371-6
[848] L. A. Hageman and R. S. Varga, ?Block iterative methods for cyclically reduced matrix equations,? Numer. Math.,6, No. 2, 106?119 (1964). · Zbl 0131.14105 · doi:10.1007/BF01386061
[849] I. N. Hajj, ?Updating method for LU factorisation,? Electron. Lett.,8, No. 7, 186?188 (1972). · doi:10.1049/el:19720137
[850] O. H. Hald, ?On the condition number of the algebraic eigenvalue problem,? Uppsala Univ., Dept. Comput. Sci., Rep. No. 49 (1973).
[851] J. H. Halton, ?Sequential Monte Carlo,? Proc. Cambridge Phil. Soc.,58, 57?78 (1962). · doi:10.1017/S0305004100036227
[852] J. H. Halton, ?Least squares Monte Carlo methods for solving linear systems of equations,? Rep. ADM-388/BNL, 9678 (1965).
[853] J. H. Halton, ?A retrospective and prospective survey of the Monte Carlo method,? SIAM Rev.,12, No. 1, 1?63 (1970). · Zbl 0193.46901 · doi:10.1137/1012001
[854] S. J. Hammarling, Latent Roots and Latent Vectors, Hilger and Watts, London (1970), Chap. XI.
[855] S. J. Hammarling, ?A note on modifications to the givens plane rotation,? J. Inst. Math. Appl.,13, No. 2, 215?218 (1974). · Zbl 0278.65037 · doi:10.1093/imamat/13.2.215
[856] J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods, Methuen, London; Wiley, New York (1965), Chap. VIII. · Zbl 0121.35503
[857] E. R. Hansen, ?On Jacobi methods and block Jacobi methods for computing matrix eigenvalues,? Lockheed, Missiles and Space Division, Sunnyvale, Calif. (1960).
[858] E. R. Hansen, ?On the Danilewski method,? J. Assoc. Comput. Mach.,10, No. 1, 102?109 (1963). · Zbl 0233.65026 · doi:10.1145/321150.321158
[859] E. R. Hansen, ?On cyclic Jacobi methods,? SIAM J. Appl. Math.,11, No. 2, 448?459 (1963). · Zbl 0118.12201 · doi:10.1137/0111032
[860] E. R. Hansen, ?Interval arithmetic in matrix computations. Part 1,? SIAM J. Numer. Anal.,2, No. 2, 308?320 (1965). · Zbl 0135.37303
[861] E. R. Hansen, ?On solving systems of equations using interval arithmetic,? Math. Comput.,22, No. 102, 374?384 (1968). · Zbl 0223.65012 · doi:10.1090/S0025-5718-1968-0229411-4
[862] E. R. Hansen, ?On the solution of linear algebraic equations with interval coefficients,? Linear Algebra Appl.,2, No. 2, 153?165 (1969). · Zbl 0185.40201 · doi:10.1016/0024-3795(69)90024-X
[863] E. R. Hansen, ?On linear algebraic equations with interval coefficients,? in: Topic in Interval Analysis, Clarendon Press, Oxford (1969), pp. 35?46.
[864] E. R. Hansen and R. Smith, ?Interval arithmetic in matrix computations. Part II,? SIAM J. Numer. Anal.,4, No. 1, 1?9 (1967). · Zbl 0209.46601 · doi:10.1137/0704001
[865] R. J. Hanson, ?Automatic error bounds for real roots of polynomials having interval coefficients,? Comput. J.,13, No. 3, 284?288 (1970). · Zbl 0195.45103 · doi:10.1093/comjnl/13.3.284
[866] R. J. Hanson and Ch. L. Lawson, ?Extensions and applications of the Householder algorithm for solving linear least squares problems,? Math. Comput.,23, No. 108, 787?812 (1969). · Zbl 0185.40701 · doi:10.1090/S0025-5718-1969-0258258-9
[867] D. J. Hardouin, ?Methode de resolution de systeme lineaire cramerien par projections successives avec orthogonalization des restes,? Rev. Franc. Inf. Rech. Opr.3, No. R-2, 15?25 (1969).
[868] W. R. Haseltine, ?Orthogonalization of a matrix,? Naval Weapons Center Tech. Note, 607?619 (1968).
[869] Masahiro Hashimoto, ?A method for solving large matrix equations reduced from Fredholm integral equations of the second kind,? J.-Assoc. Comput. Mach.,17, No. 4, 629?636 (1970). · Zbl 0211.46704 · doi:10.1145/321607.321612
[870] J. Z. Hearon, ?Symmetrizable generalized inverses of symmetrizable matrices,? J. Res. Nat. Bur. Stand.,B71, No. 4, 229?231 (1967). · Zbl 0178.03104 · doi:10.6028/jres.071B.031
[871] J. Z. Hearon, ?Generalized inverses and solutions of linear systems,? J. Res. Nat. Bur. Stand.,B72, No. 4, 303?308 (1968). · Zbl 0212.36801 · doi:10.6028/jres.072B.030
[872] J. Z. Hearon and J. W. Evans, ?On spaces and maps of generalized inverses,? J. Res. Nat. Bur. Stand.,B72, No. 2, 103?107 (1968). · Zbl 0169.04401 · doi:10.6028/jres.072B.013
[873] M. Hebgen, ?Eine scaling-invariante Pivotsuche für Intervallmatrizen,? Computing,12, No. 2, 99?106 (1974). · Zbl 0275.65007 · doi:10.1007/BF02260366
[874] M. Hebgen, ?Ein Iterationsverfahren, welches die optimalle Intervall-Einschliessung des Inversen eines M-Matrixintervalls liefert,? Computing,12, No. 2, 107?115 (1974). · Zbl 0275.65009 · doi:10.1007/BF02260367
[875] H. Heinrich, ?Bemerkung zu einem Konditionsmass für lineare Gleichungssysteme,? Z. Angew. Math. Mech.,43, No. 12, 568 (1963). · Zbl 0146.13403 · doi:10.1002/zamm.19630431213
[876] P. Henrici, Elements of Numerical Analysis, Wiley, New York-London-Sydney (1964), Chap. XV. · Zbl 0149.10901
[877] P. Henrici and K. Zimmermann, ?An estimate for the norms of certain cyclic Jacobi operators,? Linear Algebra Appl.,1, No. 4, 489?501 (1968). · Zbl 0172.18803 · doi:10.1016/0024-3795(68)90023-2
[878] R. J. Herbold, ?A generalization of a class of test matrices,? Math. Comput.,23, No. 108, 823?826 (1969). · Zbl 0183.43901 · doi:10.1090/S0025-5718-1969-0258259-0
[879] J. Herzberger, ?Zur Konvergenz intervallmässiger Iterationsverfahren,? Z. Angew. Math. Mech.,51, Sonderh., T56 (1971). · Zbl 0221.65057
[880] M. R. Hestenes, ?Iterative methods for solving linear equations,? J. Optimiz. Theory Appl.,11, No, 4, 323?334 (1973). · Zbl 0242.65035 · doi:10.1007/BF00932484
[881] M. R. Hestenes and W. Karush, ?Solution of Ax=?Bx,? J. Res. Nat. Bur. Stand.,47, 471?478 (1951). · doi:10.6028/jres.047.056
[882] M. R. Hestenes and M. L. Stein, ?The solution of linear equations by minimization,? J. Optimiz. Theory Appl.,11, No. 4, 335?359 (1973). · Zbl 0242.65043 · doi:10.1007/BF00932485
[883] Kosaburo Hirakawa, ?On the calculation of eigenvector of symmetric tridiagonal matrix,? TRU Math.,4, 44?51 (1968).
[884] R. W. Hodgkins, ?On the relation between dynamic relaxation and semiiterative matrix methods,? Numer. Math.,9, No. 5, 446?451 (1967). · Zbl 0148.39303 · doi:10.1007/BF02162158
[885] H. Hoffmann and T. A. Hoffmann, ?Lösung von Gleichungssystemen mit vielen Leerplätzen,? Wiss. Z. Tech. Univ. Dresden,17, No. 5, 1135?1136 (1968).
[886] Thuan Ho, ?Critere de regularute d’une classe de matrices quasitriangulaires et une methode pour determiner son inverse,? Tap San Toan Ly,6, No. 1, 55?57 (1967).
[887] A. S. Householder, ?Numerical analysis,? in: Lect. Mod. Math., Vol. I, Wiley, New York-London (1963), pp. 59?97.
[888] A. S. Householder, The Theory of Matrices in Numerical Analysis, Blaisdell, New York (1964), Chap. XIV. · Zbl 0161.12101
[889] A. S. Householder, ?Norms and the localization of roots of matrices,? Bull. Am. Math. Soc.,74, No. 5, 816?830 (1968). · Zbl 0169.04404 · doi:10.1090/S0002-9904-1968-12051-8
[890] A. S. Householder, ?Some applications of the theory of norms,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 27?36 (1968). · Zbl 0207.15502
[891] A. S. Householder, Quick Index for Numerical Algebra, Oak Ridge National Laboratory, Oak Ridge (1972).
[892] A. S. Householder, Quick Index for Numerical Algebra, Oak Ridge National Laboratory, Oak Ridge (1973).
[893] P. J. van der Houwen, ?On the acceleration of Richardson’s method. I. Theoretical part,? Math. Centrum Amsterdam Afd., Toegepaste Wisk., Rep. TW 104 (1967). · Zbl 0189.47702
[894] P. J. van der Houwen, ?On the acceleration of Richardson’s method. II. Numerical aspects,? Math. Centrum Amsterdam Afd., Toegepaste Wisk., Rep. TW 107 (1967). · Zbl 0189.47703
[895] P. J. van der Houwen, ?On the acceleration of Richardson’s method. III. Applications,? Math. Centrum, Amsterdam Afd., Toegepaste Wisk., Rep. TW 108 (1967). · Zbl 0189.47702
[896] J. A. Howell, ?An algorithm for the exact reduction of a matrix to Frobenius form using modular arithmetic. I,? Math. Comput.,27, No. 124, 887?904 (1973). · Zbl 0287.65029 · doi:10.1090/S0025-5718-1973-0378381-9
[897] J. A. Howell, ?An algorithm for the exact reduction of matrix to Frobenius form using modular arithmetic. II,? Math. Comput.,27, No. 124, 905?920 (1973). · Zbl 0287.65029 · doi:10.1090/S0025-5718-73-99694-4
[898] J. A. Howell and R. T. Gregory, ?An algorithm for solving linear algebraic equations using residue arithmetic. I,? BIT,9, No. 3, 220?224 (1969). · Zbl 0191.44601
[899] J. A. Howell and R. T. Gregory, ?An algorithm for solving linear algebraic equations using residue arithmetic. II,? BIT,9, No. 4, 324?337 (1969). · Zbl 0194.18104 · doi:10.1007/BF01935864
[900] J. A. Howell and R. T. Gregory, ?Solving linear equations using residue arithmetic ? algorithm. II,? BIT,10, No. 1, 23?37 (1970). · Zbl 0202.15401 · doi:10.1007/BF01940889
[901] H. Y. Hsieh and M. S. Chausi, ?A probabilistic approach to optimal pivoting and prediction of fill-in for random sparse matrices,? Tech. Rep. 400-214, Electrical Eng. Dept., New York Univ., New York (1971).
[902] H. Y. Hsieh and M. S. Chausi, ?On optimum-pivoting algorithms in sparse matrices,? IEEE Trans. Circuit Theory,19, No. 1, 93?96 (1972). · doi:10.1109/TCT.1972.1083385
[903] N. M. Huang and R. E. Gline, ?Inversion of persymmetric matrices having Toeplitz inverses,? J. Assoc. Comput. Mach.,19, No. 3, 437?444 (1972). · Zbl 0259.65032 · doi:10.1145/321707.321714
[904] O. Hübner, ?Zweiparametrige Überrelaxation,? Numer. Math.,18, No. 4, 354?366 (1972). · Zbl 0225.65042 · doi:10.1007/BF01404686
[905] G. Hufford, ?On the computation of selected eigenvalues,? J. Anal. Math.,16, 423?451 (1966). · Zbl 0143.37601 · doi:10.1007/BF02803440
[906] E. Humhal, ?A contribution to the successive overrelaxation method,? Comment. Math. Univ. Carol.,7, No. 2, 237?247 (1966).
[907] E. Humhal and J. Zitko, ?A note on the superrelaxation method,? Apl. Mat.,12, 161?170 (1967). · Zbl 0158.34202
[908] Seiiti Huzino, ?On the convergence of some linear stationary iterative processes of second degree,? Mem. Fac. Sci. Kyushu Univ.,A17, No. 2, 202?208 (1963). · Zbl 0145.40202
[909] C. Ilioi, ?Sur l’évalution de l’erreur dans la résolution des systemes linéaires,? An. Sti. Univ. Ia?i,12, Sec. la, No. 2, 313?320 (1966).
[910] C. Ilioi, ?Itérations monotones dans la methode de relaxation supérieure pour la resolution des systèmes linéaires et applications aux équations élliptiques,? An. Sti. Univ. Ia?i,14, Sec. la, No. 1, 157?168 (1968).
[911] K.-U. Jahn, ?Eine Theorie der Gleichungssysteme mit Intervall-Koeffizienten,? Z. Angew. Math. Mech.,54, No. 7, 405?412 (1974). · Zbl 0284.65022 · doi:10.1002/zamm.19740540605
[912] K. R. James, ?Convergence of matrix iterations subject to diagonal dominance,? SIAM J. Numer. Anal.,10, No. 3, 478?484 (1973). · Zbl 0255.65019 · doi:10.1137/0710042
[913] A. Jennings, ?A compact storage scheme for the solution of symmetric linear simultaneous equations,? Comput. J.,9, No. 3, 281?285 (1966). · Zbl 0142.13401 · doi:10.1093/comjnl/9.3.281
[914] A. Jennings, ?A direct iteration method of obtaining latent roots and vectors of a symmetric matrix,? Proc. Cambridge Phil. Soc.,63, No. 3, 755?765 (1967). · Zbl 0228.65029 · doi:10.1017/S030500410004175X
[915] A. Jennings, ?A sparse matrix scheme for the computer analysis of structures,? Int. J. Comput. Math.,2, No. 2, 1?21 (1968). · Zbl 0164.18803 · doi:10.1080/00207166808803022
[916] A. Jennings, ?Accelerating the convergence of matrix iterative processes,? J. Inst. Math. Appl,8, No. 1, 99?110 (1971). · Zbl 0221.65061 · doi:10.1093/imamat/8.1.99
[917] A. Jennings, ?The development and application of simultaneous iteration for eigenvalue problems,? Lect. Notes Math.,228, 297?309 (1971). · Zbl 0236.65030 · doi:10.1007/BFb0069464
[918] A. Jennings and A. D. Tuff, ?A direct method for the solution of large sparse symmetric simultaneous equations,? in: Large Sparse Sets Linear Equat., Academic Press, London-New York (1971), pp. 97?104.
[919] P. S. Jensen, ?The solution of large symmetric eigenproblems by sectioning,? SIAM J. Numer. Anal.,9, No. 4, 534?545 (1972). · Zbl 0258.65040 · doi:10.1137/0709049
[920] P. S. Jensen, ?An inclusion theorem related to inverse iteration,? Linear Algebra Appl.,6, 209?215 (1973). · Zbl 0246.15018 · doi:10.1016/0024-3795(73)90022-0
[921] A. J. Jimenez, ?Computer handling of sparse matrices,? Rep. No. TR 00.1873, IBM, New York (1969).
[922] E. L. Jones, ?Note on an alternate method for the computation of rotational energy levels of rigid asymmetric top molecules,? Comput. J.,9, No. 1, 65?66 (1966). · Zbl 0151.45903 · doi:10.1093/comjnl/9.1.65
[923] H. G. Jonson and G. A. Parks, ?Efficient solutions for linear matrix equations,? J. Struct. Div. Proc. Am. Soc Civil Eng.,96, 49?64 (1970).
[924] D. Jordan and L. F. Godbout, ?On the computation of the span of a set of vectors,? Comput. Elec. Eng.,1, No. 3, 391?400 (1973). · Zbl 0334.65026 · doi:10.1016/0045-7906(73)90005-0
[925] J. Jordan, ?Experiments on error growth associated with some linear least-squares procedures,? Math. Comput.,22, 579?588 (1968). · Zbl 0162.46801 · doi:10.1090/S0025-5718-1968-0229373-X
[926] V. N. Joshi, ?A note on the solution of rectangular linear systems by iteration,? SIAM Rev.,12, No. 3, 463?466 (1970). · Zbl 0203.47904 · doi:10.1137/1012087
[927] V. N. Joshi, ?Remarks on iterative methods for computing the generalized inverse,? Stud. Sci. Math. Hung.,8, Nos. 3?4, 457?461 (1973).
[928] V. N. Joshi and R. P. Tewarson, ?On solving ill-conditioned systems of linear equations,? Trans. N. Y. Acad. Sci.,34, No. 7, 565?571 (1972). · Zbl 0264.65032 · doi:10.1111/j.2164-0947.1972.tb02710.x
[929] J. H. Justice, ?An algorithm for inverting positive-definite Toeplitz matrices,? SIAM J. Appl Math.,23, No. 3, 289?291 (1972). · Zbl 0254.15003 · doi:10.1137/0123030
[930] H. Kääb, ?Einige Möglichkeiten der Pivotsuche beim Gaussschen Algorithmus,? Z. Angew. Math, und Mech.,50, Sonderh. 1?4, T56-T57 (1970). · Zbl 0195.44902 · doi:10.1002/zamm.19700500122
[931] B. Kägström and A. Ruhe, ?An algorithm for numerical computation of the Jordan normal form of a complex matrix,? Inst. Math. and Statistics, Dept. Inform. Process. Rep. UMINF-51, 74 (1974). · Zbl 0434.65020
[932] W. Kahan, ?Accurate eigenvalues of a symmetric tridiagonal matrix,? Computer Sci. Dept., Stanford Univ. Tech. Rep. CS 41 (1966).
[933] W. Kahan, ?Relaxation methods for an eigenproblem,? Computer Sci. Dept., Stanford Univ. Tech. Rep. CS 44 (1966).
[934] W. Kahan, ?Relaxation methods for semidefinite systems,? Computer Sci. Dept., Stanford Univ. Tech. Rep. CS 45 (1966).
[935] W. Kahan, ?Numerical linear algebra,? Can. Math. Bull.,9, No. 6, 757?801 (1966). · Zbl 0236.65025 · doi:10.4153/CMB-1966-083-2
[936] W. Kahan and J. Varah, ?Two working algorithms for the eigenvalues of a symmetric tridiagonal matrix,? Computer Sci. Dept., Stanford Univ. Tech. Rep. CS 43 (1966).
[937] H. F. Kaiser, ?A method for determining eigenvalues,? Notices Am. Math. Soc.,10, 371 (1963).
[938] H. F. Kaiser, ?A method for determining eigenvalues,? SIAM J. Appl. Math.,12, No. 1, 238?248 (1964). · Zbl 0122.12203 · doi:10.1137/0112023
[939] H. F. Kaiser, ?The JK method: a procedure for finding the eigenvectors and eigenvalues of a real symmetric matrix,? Comput. J.,15, No. 3, 271?273 (1972). · Zbl 0243.65009 · doi:10.1093/comjnl/15.3.271
[940] H. Kamasova, ?An algorithm for the inversion of partitioned matrices,? Apl. Mat.,15, No. 6, 399?406 (1970). · Zbl 0194.05904
[941] H. Kamasova and A. Simek, ?Metoda inverze matrice rozdelene na bloky,? Apl. Mat.,14, No. 2, 105?114 (1969).
[942] H. Kamasova and A. Simek, ?Inversion of quasitriangular matrices,? Apl. Mat.,15, No. 2, 146?148 (1970). · Zbl 0194.05904
[943] W. J. Kammerer and R. S. Varga, ?On asymptotically best norms for powers of operators,? Numer. Math.,20, No. 2, 93?98 (1972). · Zbl 0232.65038 · doi:10.1007/BF01404399
[944] S. Kaniel, ?Estimates for some computational techniques in linear algebra,? Math. Comput.,20, No. 95, 369?378 (1966). · doi:10.1090/S0025-5718-1966-0234618-4
[945] S. Kaniel and J. Stein, ?Least-square acceleration of iterative methods for linear equations,? J. Optimiz. Theory Appl.,14, No. 4, 431?437 (1974). · Zbl 0272.65022 · doi:10.1007/BF00933309
[946] L. V. Kantorovich, ?The method of successive approximation for functional equations,? Acta Math.,71, 62?97 (1939).
[947] Ilkka Karasalo, ?A criterion for truncation of the QR-decomposition algorithm for the singular linear least squares problem,? BIT,14, No. 2, 156?166 (1974). · Zbl 0282.65030 · doi:10.1007/BF01932945
[948] V. Kartheus, ?Zur intervallanalytischen Behandlung linearer Gleichungssysteme,? Mitt. Ges. Math. Datenverarb., No. 16, 27 (1972).
[949] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin (1966), Chap. XX. · Zbl 0148.12601
[950] I. J. Katz, ?Wiegmann type theorems for EPr matrices,? Duke Math. J.,32, No. 3, 423?427 (1965). · Zbl 0168.03102 · doi:10.1215/S0012-7094-65-03242-4
[951] I. J. Katz and M. H. Pearl, ?On EPr and normal EPr matrices,? J. Res. Nat. Bur. Stand.,B70, No. 1, 47?77 (1966). · Zbl 0138.01401 · doi:10.6028/jres.070B.004
[952] L. Kaufman, ?The LZ algorithm to solve the generalized eigenvalue problem,? SIAM J. Numer. Anal.,11, No. 5, 997?1024 (1974). · Zbl 0294.65025 · doi:10.1137/0711078
[953] R. G. Kayel, ?A linear model for Gauss elimination,? Int. J. Comput. Math.,3, Nos. 2?3, 279?298 (1972). · Zbl 0264.65028 · doi:10.1080/00207167208803068
[954] H. B. Keller, ?Special block iterations with applications to Laplace and biharmonic difference equations,? SIAM Rev.,2, No. 4, 277?287 (1960). · Zbl 0097.11501 · doi:10.1137/1002060
[955] H. B. Keller, ?On the solution of singular and semidefinite linear systems by iteration,? SIAM J. Numer. Anal.,2, No. 2, 281?290 (1965). · Zbl 0135.37503
[956] J. B. Keller, ?Factorization of matrices by least squares,? Biometrika,49, 239?242 (1962). · Zbl 0106.34402 · doi:10.1093/biomet/49.1-2.239
[957] R. B. Kellogg, ?Another alternating-direction-implicit method,? SIAM J. Appl. Math.,11, No. 4, 976?979 (1963). · Zbl 0214.14703 · doi:10.1137/0111071
[958] R. B. Kellogg, ?An alternating direction method for operator equations,? SIAM J. Appl. Math.,12, No. 4, 848?854 (1964). · Zbl 0125.35601 · doi:10.1137/0112072
[959] R. B. Kellogg and J. Spanier, ?On optimal alternating direction parameters for singular matrices,? Math. Comput.,19, No. 91, 448?452 (1965). · Zbl 0208.18203 · doi:10.1090/S0025-5718-1965-0184442-5
[960] H. P. M. van Kempen, ?On the convergence of the classical Jacobi method for real symmetric matrices with nondistinct eigenvalues,? Numer. Math.,9, No. 1, 11?18 (1966). · Zbl 0229.65037 · doi:10.1007/BF02165224
[961] H. P. M. van Kempen, ?On the quadratic convergence of the special cyclic Jacobi method,? Numer. Math.,9, No. 1, 19?22 (1966). · Zbl 0229.65038 · doi:10.1007/BF02165225
[962] I. M. Khabaza, ?An iterative least-square method suitable for solving large sparse matrices,? Comput. J.,6, No. 2, 202?206 (1963). · Zbl 0131.33901 · doi:10.1093/comjnl/6.2.202
[963] A. Kielbasinski, ?On the iterative procedures of best strategy for inverting a self-adjoint positivedefinite bounded operator in Hubert space,? Stud. Math.,24, No. 1, 13?23 (1964). · Zbl 0187.38203
[964] A. Kielbasinski, ?Oszacowanie bledu w metodzie eliminacji,? Rocz. Pol. Tow. Mat., Ser. 3,1, 9?21 (1973).
[965] A. Kielbasinski, ?Algorytm sumowania z poprawkami i niektore jego zastosowania,? Rocz. Pol. Tow. Mat., Ser. 3,1, 23?41 (1973).
[966] A. Kielbasinski and J. Jankowska, ?Fehleranalyse der Schmidtschen und Powellschen Orthonormalisierungsverfahren,? Z. Angew. Math. Mech.,54, No. 4, T223 (1974). · Zbl 0317.65017 · doi:10.1002/zamm.197405412129
[967] A. Kielbasinski, G. Wozniakowsky, and H. Wozniakowski, ?Algorytmizacja metod najlepszej strategii dla wielkich ukladow rownan o symetrycznej, dodatnio okreslonej macierzy,? Rocz. Pol. Tow. Mat.,Ser. 3,1, 47?68 (1973).
[968] D. R. Kincaid, ?Norms of the successive overrelaxation method,? Math. Comput.,26, No. 118, 345?357 (1972). · Zbl 0251.65026 · doi:10.1090/S0025-5718-1972-0311089-3
[969] D. R. Kincaid, ?A class of norms of iterative methods for solving systems of linear equations,? Numer. Math.,20, No. 5, 392?408 (1973). · Zbl 0254.65023 · doi:10.1007/BF01402562
[970] D. R. Kincaid, ?On complex second-degree iterative methods,? SIAM J. Numer. Anal.,11, No. 2, 211?218 (1974). · Zbl 0289.65016 · doi:10.1137/0711020
[971] D. R. Kincaid and D. M. Young, ?The modified successive overrelaxation method with fixed parameters,? Math. Comput.,26, No. 119, 705?717 (1972). · Zbl 0264.65029 · doi:10.1090/S0025-5718-1972-0331746-2
[972] A. Klinger, ?Approximate pseudoinverse solutions to ill-conditioned linear systems,? J. Optimiz. Theory Appl.,2, No. 2, 117?124 (1968). · Zbl 0187.09604 · doi:10.1007/BF00929587
[973] F. Königshofer, ?Das modifizierte Ergänzungsverfahren zur Invertierung von Matrizen,? Computing,8, Nos. 3?4, 221?240 (1971). · Zbl 0228.65025 · doi:10.1007/BF02234105
[974] A. Korganoff and M. Pavel-Parvu, ?Elements de théorie des matrices carrées et rectangulaires en analyse numerique,? Méthodes de Calcul Numerique, Dunod, Paris (1967).
[975] C. N. Kourogenis, ?The eigenvalue problem and Jacobeanlike methods for its solution,? Bull. Soc. Math. Grece,11, No. 1, 97?131 (1970).
[976] Z. Kovarik, ?Some iterative methods for improving orthonormality,? SIAM J. Numer. Anal.,7, No. 3, 386?389 (1970). · Zbl 0217.21501 · doi:10.1137/0707031
[977] J. Kowalik, ?Iterative methods for large systems of linear equations in matrix structural analysis,? Int. Shipbuild. Progr.,13, No. 138, 59?68 (1966).
[978] H. Krämer, ?Eine Vereinfachung des Verfahrens von Le Verrier-Horst zur Aufstellung des charakteristischen Polynoms einer Matrix,? Z. Angew. Math. Mech.,45, No. 5, 297?304 (1965). · Zbl 0135.37504 · doi:10.1002/zamm.19650450504
[979] R. Krautstengl, ?K problemu urychlovani konvergence jednoducheho iteracnicho procesu pro reseni soustavy linearnich rovnic,? Apl. Mat.,9, No. 6, 399?109 (1964).
[980] R. Krawczyk, ?Iterative Verbesserung von Schranken für Eigenwerte und Eigenvektoren reeler Matrizen,? Z. Angew. Math. Mech.,48, No. 8, Sonderh., T80-T83 (1968).
[981] R. Krawczyk, ?Fehlerabschätzung reeller Eigenwerte und Eigenvecktoren von Matrizen,? Computing,4, No. 4, 281?293 (1969). · Zbl 0181.17205 · doi:10.1007/BF02235463
[982] R. Krawczyk, ?Verbesserung von Schranken für Eigenwerte und Eigenvektoren von Matrizen,? Computing,5, No. 3, 200?206 (1970). · Zbl 0199.49804 · doi:10.1007/BF02248020
[983] R. Krawczyk, ?Einschliessung von Nullstellen mit Hilfe einer Intervallarithmetik,? Computing,5, 356?370 (1970). · Zbl 0206.46503 · doi:10.1007/BF02252330
[984] R. Krawczyk, ?Abbrechkriterium für Iterationsverfahren,? Z. Angew. Math. Mech.,52, No. 5, 227?232 (1972). · doi:10.1002/zamm.19720520403
[985] B. Kredell, ?On complex successive overrelaxation,? BIT,2, 143?152 (1962). · Zbl 0112.07602 · doi:10.1007/BF01957329
[986] Th. Kreifelts, ?Über vollautomatische Erfassung und Abschätzung von Rundungsfehlern in arithmetischen Prozessen,? Ber. Ges. Math. Datenverarb., No. 62, 98 (1972). · Zbl 0251.65035
[987] Th. Kreifelts, ?Über Pivot-Strategien bei der Lösung linearer Gleichungssysteme,? Computing,10, Nos. 1?2, 167?175 (1972). · Zbl 0262.65023 · doi:10.1007/BF02242391
[988] G. Kron, Diakoptics, MacDonald, London (1963).
[989] F. Krückeberg, ?Inversion von Matrizen mit Fehlererfassung,? Z. Angew. Math. Mech.,46, Sonderh., T69-T71 (1966).
[990] F. Krückeberg, ?Bemerkungen zur Intervall-Analysis,? Apl. Mat.,13, No. 2, 152?153 (1968). · Zbl 0198.49202
[991] V. N. Kublanovskaja, ?On an approach to the solution of the generalized latent value problem for X-matrices,? SIAM J. Numer. Anal.,7, No. 4, 532?537 (1970). · Zbl 0225.65048 · doi:10.1137/0707043
[992] V. N. Kublanovskaja, ?Application of the orthogonal transformations to the solution of one extremal problem,? Proc. IFIP Congr. 71, Ljubljana, 1971, Vol. 2, North-Holland, Amsterdam-London (1972), pp. 1311?1316.
[993] D. J. Kuck and A. H. Sameh, ?Parallel computation of eigenvalues of real matrices,? Proc. IFIP Congr. 71, Ljubljana, 1971, Vol. 2 (1972), pp. 1266?1272.
[994] A. Kühne, ?Ein Jacobi-Verfahren für normale Matrizen,? Diss. Dokt. Math. Eidgenoss. Tech. Hochsch. Zürich (1974).
[995] Fr. Kuhnert, ?Über die genaherte Berechnung von Eigenwerten durch Pseudostöriteration,? Wiss. Beitr. Martin-Luther Univ. Halle-Wittenberg,M, No. 1, 71?80 (1968). · Zbl 0184.37201
[996] Fr. Kuhnert, ?Über einige Verfahren zur Berechnung von Matrizeneigenwerten,? Wiss. Z. Techn. Hochsch. Kral-Marx-Stadt,10, No. 5, 511?513 (1968). · Zbl 0276.65016
[997] Fr. Kuhnert, ?Entwicklungstendenzen in der Numerischen Mathematik,? Wiss. Z. Techn. Hochsch. Karl-Marx-Stadt,15, Sonderausg. I (Teil I), 35?41 (1973). · Zbl 0287.65002
[998] U. Kulisch, ?Über reguläre Zerlegungen von Matrizen und einige Anwendungen,? Numer. Math.,11 No. 5, 444?449 (1968). · Zbl 0165.50202 · doi:10.1007/BF02161890
[999] U. Kulisch, ?Grundzüge einer Intervallrechnung,? Überblicke Math.,2, 51?98 (1969).
[1000] H. E. Kulsrud, ?A practical technique for the determination of the optimum relaxation factor of the successive over-relaxiation method,? Commun. ACM,4, No. 4, 184?187 (1961). · Zbl 0099.11001 · doi:10.1145/355578.366504
[1001] Fr. Laborde, ?Recherche des valeurs propres d’une matrice: algorithme MR,? C. R. Acad. Sci.,261, No. 4, A871-A874 (1965). · Zbl 0132.36302
[1002] Fr. Laborde, ?Sur un probleme inverse d’un probleme de valeurs propres,? C. R. Acad. Sci.,268, No. 3, A153-A156 (1969). · Zbl 0174.47001
[1003] C. D. LaBudde, ?The reduction of an arbitrary real square matrix to tridiagonal form using similarity transformations,? Math. Comput.,17, No. 84, 433?437 (1963). · doi:10.1090/S0025-5718-1963-0156455-9
[1004] C. D. LaBudde, ?Two new classes of algorithms for finding the eigenvalues and eigenvectors of real symmetric matrices,? J. Assoc. Comput. Mach.,11, No. 1, 53?58 (1964). · Zbl 0124.33003 · doi:10.1145/321203.321210
[1005] C. D. LaBudde, ?A new algorithm for diagonalizing a real symmetric matrix,? Math. Comput.,18, No. 85, 118?123 (1964). · doi:10.1090/S0025-5718-1964-0160319-5
[1006] C. D. LaBudde and G. R. Verma, ?On the computation of a generalized inverse of a matrix,? Q. Appl. Math.,27, No. 3, 391?395 (1969). · Zbl 0194.18202 · doi:10.1090/qam/253541
[1007] H. O. Lancaster, ?The Helmert matrices,? Am. Math. Mon.,72, No. 1, 4?12 (1965). · Zbl 0124.01102 · doi:10.2307/2312989
[1008] P. Lancaster, ?A generalized Rayleigh-quotient iteration for lambda matrices,? Arch. Ration. Mech. Anal.,13, No. 4, 309?322 (1961). · Zbl 0105.31705 · doi:10.1007/BF00277446
[1009] P. Lancaster, ?Some applications of the Newton-Raphson method to nonlinear matrix problems,? Proc. R. Soc.,A271, No. 1346, 324?331 (1963). · Zbl 0194.18301 · doi:10.1098/rspa.1963.0021
[1010] P. Lancaster, ?On eigenvalues of matrices dependent on a parameter,? Numer. Math.,6, No. 5, 377?387 (1964). · Zbl 0133.26201 · doi:10.1007/BF01386087
[1011] P. Lancaster, ?Algorithms for ?-matrices,? Numer. Math.,6, No. 5, 388?394 (1964). · Zbl 0246.65016 · doi:10.1007/BF01386088
[1012] P. Lancaster, ?-Matrices and Vibrating Systems, Pergamon Press, Oxford (1966), Chap. XIII.
[1013] P. Lancaster, Theory of Matrices, Academic Press, New York-London (1969), Chap. XII.
[1014] P. Lancaster, ?A note onsubmultiplicative norms,? Numer. Math.,19, No. 3, 206?208 (1972). · Zbl 0227.15007 · doi:10.1007/BF01404689
[1015] P. Lancaster and H. K. Farahat, ?Norms on direct sums and tensor products,? Math. Comput.,26, No. 118, 401?414 (1972). · Zbl 0247.65030 · doi:10.1090/S0025-5718-1972-0305099-X
[1016] C. E. Langenhop, ?Ongeneralized inverses of matrices,? SIAM J. Appl. Math.,15, No. 5, 1239?1246 (1967). · Zbl 0155.35406 · doi:10.1137/0115105
[1017] W. E. Langlois, ?Conditions for termination of the method of steepest descent after a finite number of iterations,? IBM J. Res. Develop.,10, 98?99 (1966). · Zbl 0132.36202 · doi:10.1147/rd.101.0098
[1018] M. LaPorte and J. Vignes, ?Etude statistique des erreurs dans l’arithmétique des ordinateurs; application au contrôle des resultats d’algorithmes numérique,? Numer. Math.,23, No. 1, 63?72 (1974). · Zbl 0278.65043 · doi:10.1007/BF01409991
[1019] M. LaPorte and J. Vignes, ?Méthode numérique de détection de la singularité d’une matrice,? Numer. Math.,23, No. 1, 73?81 (1974). · Zbl 0302.65022 · doi:10.1007/BF01409992
[1020] M. LaPorte and J. Vignes, ?Algorithmes numeriques, analyse et mise en oeuvre. I. Arithmétique des ordinateurs systemes linéaires,? Edition Tech. (1974).
[1021] M. H. E. Larcombe, ?A list processing approach to the solution of large sparse sets of matrix equations and the factorization of the overall matrix,? in: Large Sparse Sets of Linear Equations, Academic Press, London-New York (1971), pp. 25?39.
[1022] L. J. Lardy, ?An extrapolated Gauss-Seidel iteration for Hessenberg matrices,? Math. Comput.,27, No. 124, 921?926 (1973). · Zbl 0271.65025 · doi:10.1090/S0025-5718-1973-0327012-2
[1023] L. J. Larsen, ?A modified inversion procedure for product form of inverse in linear programming codes,? Commun. ACM,5, No. 7, 382?383 (1962). · Zbl 0106.10305 · doi:10.1145/368273.368283
[1024] W. S. LaSor, ?Test matrix for inversion,? Commun. ACM,6, No. 3, 102 (1963). · doi:10.1145/366274.366307
[1025] C. Lebaud, ?Remarques sur la convergence de la methode QR,? Rev. Franc. Inf. Rech. Oper.,2, No. 13, 103?112 (1968). · Zbl 0208.40105
[1026] C. Lebaud, ?L’algorithme double Q-R avec ?shift?,? Numer. Math.,16, No. 2, 163?180 (1970). · Zbl 0195.16801 · doi:10.1007/BF02308869
[1027] C. Lebaud, ?On the Q \(\cdot\)R algorithm with shift,? Int. J. Comput. Math.,2, No. 4, 343?358 (1970). · Zbl 0214.14705 · doi:10.1080/00207167008803045
[1028] H. B. Lee, ?An implementation of Gaussian elimination for sparse systems of linear equations,? in: Sparse Matrix Proceedings, R. A. Willoughby (ed.), RA I No. 11707, IBM Corp., Thomas J. Watson Res. Center, Yorktown Heights, New York (1969), pp. 75?84.
[1029] J. Legras, ?Remarques sur la resolution des grands systemes lineaires par technique iterative,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 227?236 (1968).
[1030] R. S. Lehman, ?Dynamic programming and Gaussian elimination,? J. Math. Anal. Appl.,5, No. 3, 499?501 (1962). · Zbl 0122.35602 · doi:10.1016/0022-247X(62)90021-5
[1031] Orjan Leringe and Per-Ake Wedin, ?A comparison between different methods to compute a vector x which minimizes ?Ax-B?2 when Gx=h,? Lund. Univ. Dept. Comput. Sci. (1970).
[1032] M. Levy, ?Quelques remarques sur les erreurs dans la méthode de Lanczos pour la recherche des valeurs propres d’une matrice,? Rev. Franc. Traitement Inform. Chiffres,4, No. 2, 87?100 (1961). · Zbl 0104.10004
[1033] M. Levy, ?Contribution a l’étude de la méthode de Lanczos,? These Doct. 3-e Cycl. Math. Appl. Fac. Sci. Univ. Grenoble (1961).
[1034] R. Levy, ?Resequencing of the structural stiffness matrix to improve computational efficiency,? JPL Q. Tech. Rev.,1, 61?70 (1971).
[1035] T. O. Lewis, T. L. Boullion, and P. L. Odell, ?A bibliography on generalized matrix inverses,? Proc. Symp. on Theory and Appl. of Generalized Inverses of Matrices, Texas Tech. Coll., Lubbock, Texas (1968), pp. 283?315. · Zbl 0185.07701
[1036] P. Liebl, ?Einige Bemerkungen zur numerischen Stabilität von Matrizeniterationen,? Apl. Mat.,10, No. 3, 249?254 (1965). · Zbl 0239.65036
[1037] P. Liebl and M. Novakova, ?A method for dealing with ill-conditioned symmetric linear systems,? Apl. Mat.,15, No. 6, 407?412 (1970). · Zbl 0221.65074
[1038] M. H. Lietzke, R. W. Stoughton, and M. P. Lietzke, ?A comparison of several methods for inverting large symmetric positive-definite matrices,? Math. Comput.,18, No. 87, 449?456 (1964). · Zbl 0122.12201 · doi:10.1090/S0025-5718-1964-0166914-1
[1039] M. Lignac, ?Méthodes de perturbations pour la résolution des systèmes linéaires mal conditionnés,? 3-e Congr. Calcul et Traitem. Inform. AFCALTI, Toulouse, 1963, Paris (1965), pp. 109?115.
[1040] J. Linke, ?Methoden zur Lösungseinschliessung durch monotone oder alternierende Iterationsfolgen bei linearen Gleichungssystemen,? Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt,13, No. 1, 17?29 (1971). · Zbl 0288.65030
[1041] G. Loizou, ?An empirical estimate of the relative error of the computed solution x of Ax=b,? Comput. J.,11, No. 1, 91?94 (1968). · Zbl 0164.45103 · doi:10.1093/comjnl/11.1.91
[1042] G. Loizou, ?On the quadratic convergence of the Jacobi method for normal matrices,? Comput. J.,15, No. 3, 274?276 (1972). · Zbl 0243.65012 · doi:10.1093/comjnl/15.3.274
[1043] L. de Loringhoven, ?Inversion d’une matrice carrée symetrique par double factorisation,? Constr. Metall.,5, No. 1, 61?65 (1968).
[1044] W. S. Loud, ?Generalized inverse and generalized Green’s functions,? SIAM J. Appl. Math.,14, No. 2, 342?369 (1966). · Zbl 0142.00303 · doi:10.1137/0114030
[1045] V. Lovass-Nagy and D. L. Powers, ?A relation between the Moore -Penrose and commuting reciprocal inverses,? SIAM J. Appl. Math.,24, No. 1, 44?49 (1973). · Zbl 0234.15007 · doi:10.1137/0124006
[1046] D. G. Luenberger, ?Hyperbolic pairs in the method of conjugate gradients,? SIAM J. Appl. Math.,17, No. 6, 1263?1267 (1969). · Zbl 0187.09704 · doi:10.1137/0117118
[1047] D. G. Luenberger, ?The conjugate residual method for constrained minimization problems,? SIAM J. Numer. Anal.,7, No. 3, 390?398 (1970). · Zbl 0209.17601 · doi:10.1137/0707032
[1048] L. Luksan, ?A collection of programs for operations involving sparse matrices,? Res. Rep. Z-483, Inst. Radio Eng. and Electronics, CSAV, Prague (1972).
[1049] H. A. Luther, ?An N-step method for the solution of a class of simultaneous linear equations,? Tex. J. Sci.,17, No. 2, 224?227 (1965).
[1050] R. E. Lynch and J. R. Rice, ?Convergence rates of ADI methods with smooth initial error,? Math. Comput.,22, No. 102, 311?335 (1968). · Zbl 0252.65080
[1051] R. E. Lynch, J. R. Rice, and D. H. Thomas, ?Direct solution of partial difference equations by tensor product methods,? Numer. Math.,6, No. 3, 185?199 (1964). · Zbl 0126.12703 · doi:10.1007/BF01386067
[1052] R. E. Lynch, J. R. Rice, and D. H. Thomas, ?Tensor product analysis of partial difference equations,? Bull. Am. Math. Soc.,70, No. 3, 378?384 (1964). · Zbl 0126.12704 · doi:10.1090/S0002-9904-1964-11105-8
[1053] R. E. Lynch, J. R. Rice, and D. H. Thomas, ?Tensor product analysis of alternating direction implicit methods,? SIAM J. Appl. Math.,13, No. 4, 995?1006 (1965). · Zbl 0137.33303 · doi:10.1137/0113067
[1054] M. S. Lynn, ?Some inframax bounds for the spectral radii of splittings of H-matrices,? Numer. Math.,5, No. 2, 152?174 (1963). · Zbl 0115.11302 · doi:10.1007/BF01385887
[1055] M. S. Lynn, ?On the equivalence of SOR, SSOR and USSOR as applied to ?1-ordered systems of linear equations,? Comput. J.,7, No. 1, 72?75 (1964). · Zbl 0134.32705 · doi:10.1093/comjnl/7.1.72
[1056] M. S. Lynn, ?On the round-off error in the method of successive overrelaxation,? Math. Comput.,18, No. 85, 36?49 (1964). · Zbl 0115.34301 · doi:10.1090/S0025-5718-1964-0162364-2
[1057] J. -F. Maitre, ?Evaluation d’une borne d’erreur pour la résolution d’un système linéaire symetrique par la methode de Cholesky (calculs en virgule fixe),? C. R. Acad. Sci.,256, No. 20, 4150?4152 (1963).
[1058] J. -F. Maitre, ?Contribution to the study of the numerical solution of an ill-conditioned linear system by Gaussian strategies,? Thesis Univ. Besancon (1964).
[1059] J.-F. Maitre, ?Norme composée et norme associée generalisée d’une matrice,? Numer. Math.,10, No. 2, 132?141 (1967). · Zbl 0155.35401 · doi:10.1007/BF02174145
[1060] J.-F. Maitre, ?Sur une classe de normes et l’analyse à postériori d’un système linéaire,? Numer. Math.,12, No. 2, 106?110 (1968). · Zbl 0184.37502 · doi:10.1007/BF02173404
[1061] J.-F. Maitre, ?Approximation de rang donne dans un espace de matrices,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 105?110 (1968). · Zbl 0207.15503
[1062] J.-F. Maitre and Huu Vinh Nguyen, ?Valeurs singulieres généralisées et meilleure approximation de rang d’un operateur lineaire,? C. R. Acad. Sci.,262, No. 9, A502-A504 (1966). · Zbl 0133.38104
[1063] J. -F. Maitre and Huu Vinh Nguyen, ?Evaluation de la distance d’une matrice a l’ensemble des matrices de rang r,? C. R. Acad. Sci.,262, No. 16, A910-A912 (1966). · Zbl 0171.36001
[1064] M. A. Malcolm and J. Palmer, ?A fast method for solving a class of tridiagonal linear systems,? Commun. ACM,17, No. 1, 14?17 (1974). · Zbl 0271.65023 · doi:10.1145/360767.360777
[1065] O. L. Mangasarian, ?Characterizations of real matrices of monotone kind,? SIAM Rev.,10, No. 4, 439?441 (1968). · Zbl 0179.05102 · doi:10.1137/1010095
[1066] O. L. Mangasarian, ?A convergent splitting of matrices,? Numer. Math.,15, No. 4, 351?353 (1970). · Zbl 0185.40104 · doi:10.1007/BF02165128
[1067] O. L. Mangasarian, ?Convergent generalized monotone splitting of matrices,? Math. Comput.,25, No. 116, 649?653 (1971). · Zbl 0227.65022 · doi:10.1090/S0025-5718-1971-0298907-1
[1068] O. L. Mangasarian, ?Monotone splitting of matrices,? Linear Algebra Appl.,8, No. 1, 43?56 (1974). · Zbl 0275.65012 · doi:10.1016/0024-3795(74)90007-X
[1069] G. I. Marchuk, ?Methods and problems of computational mathematics,? Actes Congr. Int. Math. I, Gauthier-Villars, Paris (1971), pp. 151?161.
[1070] G. I. Marchuk, ?On the theory of the splitting up method,? in: Numerical Solution of Partial Differential Equations. II, Academic Press, New York-London (1971), pp. 469?500.
[1071] G. I. Marchuk and Yu. A. Kuznetsov, ?Stationary iterative methods for the solution of systems of linear equations with singular matrices,? Gatlinburg VI, Symposium on Numerical Algebra, München (1974).
[1072] M. D. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston (1964), Chap. XVI. · Zbl 0126.02404
[1073] I. Marek, ?On extrapolation of linear iterative methods.? Gatlinburg VI, Symposium on Numerical Algebra, München (1974).
[1074] H. M. Markowitz, ?The elimination form of the inverse and its application to linear programming,? Manag. Sci.,3, No. 3, 255?269 (1957). · Zbl 0995.90592 · doi:10.1287/mnsc.3.3.255
[1075] K. Marks and J. Bienkowski, ?Metoda eliminacji uporzadkowanej,? Energetyka (Polska),21, No. 1 (1967), Biul. Inst. Energ.,9, Nos. 1?2, 3?6 (1967).
[1076] S. Marlow and J. K. Reid, ?Fortran subroutines for the solution of linear equations, inversion of matrices and evaluation of determinants,? AERE Rep. R6899, HMSO, London (1971).
[1077] D. Marsal, ?Konvergenzbeschleunigte Iteration von linearen Gleichungssystemen bei Divergenz des klassischen Verfahrens unter besonderer Berücksichtigung von Randwertproblemen,? Computing,4, No. 3, 234?245 (1969). · Zbl 0208.18201 · doi:10.1007/BF02234772
[1078] A. W. Marshall and I. Olkin, ?Scaling of matrices to achieve specified row and column sums,? Numer. Math.,12, No. 1, 83?90 (1968). · Zbl 0165.17401 · doi:10.1007/BF02170999
[1079] R. S. Martin, G. Peters, and J. H. Wilkinson, ?Symmetric, decomposition of a positive definite matrix,? Numer. Math.,7, No. 5, 362?383 (1965). · Zbl 0135.37402 · doi:10.1007/BF01436249
[1080] R. S. Martin, G. Peters, and J. H. Wilkinson, ?Iterative refinement of the solution of a positive-definite system of equations,? Numer. Math.,8, No. 3, 203?216 (1966). · Zbl 0158.33804 · doi:10.1007/BF02162558
[1081] R. S. Martin, G. Peters, and J. H. Wilkinson, ?The QR algorithm for real Hessenberg matrices,? Numer. Math.,14, No. 3, 219?231 (1970). · Zbl 0194.46901 · doi:10.1007/BF02163331
[1082] R. S. Martin, C. Reinsch, and J. H. Wilkinson, ?Householder’s tridiagonalization of a symmetric matrix,? Numer. Math.,11, No. 3, 181?195 (1968). · Zbl 0176.13402 · doi:10.1007/BF02161841
[1083] R. S. Martin, C. Reinsch, and J. H. Wilkinson, ?The QR algorithm for band symmetric matrices,? Numer. Math.,16, No. 2, 85?92 (1970). · Zbl 0211.46803 · doi:10.1007/BF02308862
[1084] R. S. Martin and J. H. Wilkinson, ?Symmetric decomposition of positive definite band matrices,? Numer. Math.,7, No. 5, 355?361 (1965). · Zbl 0137.32806 · doi:10.1007/BF01436248
[1085] R. S. Martin and J. H. Wilkinson, ?Solution of symmetric and unsymmetric band equations and the calculation of eigenvectors of band matrices,? Numer. Math.,9, No. 4, 279?301 (1967). · Zbl 0168.13304 · doi:10.1007/BF02162421
[1086] R. S. Martin and J. H. Wilkinson, ?Reduction of the symmetric eigenproblem Ax=?Bx and related problems to standard form,? Numer. Math.,11, No. 2, 99?110 (1968). · Zbl 0162.46901 · doi:10.1007/BF02165306
[1087] R. S. Martin and J. H. Wilkinson, ?Similarity reduction of a general matrix to Hessenberg form,? Numer. Math.,12, No. 5, 349?368 (1968). · Zbl 0184.37504 · doi:10.1007/BF02161358
[1088] R. S. Martin and J. H. Wilkinson, ?The modified LR algorithm for complex Hessenberg matrices,? Numer. Math.,12, No. 5, 369?376 (1968). · Zbl 0184.37505 · doi:10.1007/BF02161359
[1089] R. S. Martin and J. H. Wilkinson, ?The implicit QL algorithm,? Numer. Math.,12, No. 5, 377?383 (1968). · Zbl 0176.46304 · doi:10.1007/BF02161360
[1090] P. Marzulli, ?Su certe matrici utilizzabili come matrici test,? Calcolo,8, Nos. 1?2, 81?88 (1971). · Zbl 0222.15005 · doi:10.1007/BF02575576
[1091] E. Massa, ?Sulla determinazione di autovalori con moduli poco diversi e delle relative autoennuple mediante procedimento di iterazione,? Ist. Lombardo Accad. Sci. Lett., Rend.,A97, 394?416 (1963).
[1092] K. Marthiak, ?Eine Ergänzung zum Krylovschen Verfahren zur Berechnung der Eigenwerte selstadjungierter Operatoren endlich dimensionaler Raume,? Arch. Math.,18, No. 2, 197?200 (1967). · Zbl 0171.13501 · doi:10.1007/BF01899646
[1093] O. Mayer, ?Über die in der Intervallrechnung auftretenden Räume und einige Anwendungen,? Diss., Univ. Karlsruhe (1968).
[1094] O. Mayer, ?Über die intervallmässige Durchführung einiger Iterationsverfahren,? Z. Angew. Math. Mech.,50, Sonderh. 1?4 T65-T66 (1970). · Zbl 0199.49803 · doi:10.1002/zamm.19700500127
[1095] O. Mayer, ?Über eine Klasse komplexer Intervallgleichungssysteme mit iterationsfahiger Gestalt,? Computing,6, Nos. 1?2, 104?106 (1970). · Zbl 0214.40906 · doi:10.1007/BF02241738
[1096] O. Mayer, ?On the determinant of inclusion sets for the solution of linear systems of equations with coefficients subject to error,? Elektron. Datenverarb., 164?167 (1970).
[1097] O. Mayer, ?Über intervallmassige Iterationsverfahren bei linearen Gleichungssystemen und allgemeineren Intervallgleichungssystemen,? Z. Angew. Math. Meeh.,51, No. 2, 117?124 (1971). · Zbl 0236.65026 · doi:10.1002/zamm.19710510206
[1098] D. Q. Mayne, ?An algorithm for the calculation of the pseudoinverse of a singular matrix,? Comput. J.,9, No. 3, 312?317 (1966). · Zbl 0152.35401 · doi:10.1093/comjnl/9.3.312
[1099] D. Q. Mayne, ?On the calculation of pseudoinverses,? IEEE Trans. Autom. Control,14, No. 2, 204?205 (1969). · doi:10.1109/TAC.1969.1099150
[1100] R. B. McCammon, ?Half rotations in n-dimensional Euclidean space,? Commun. ACM,9, No. 9, 688?689 (1966). · Zbl 0142.11604 · doi:10.1145/365813.365841
[1101] Ch. McCarthy and G. Strang, ?Optimal conditioning of matrices,? SIAM J. Numer. Anal.,10, No. 2, 370?388 (1973). · Zbl 0314.65018 · doi:10.1137/0710034
[1102] L. K. McDowell, ?Variable successive over-relaxation,? Dept. Comput. Sci., Univ. Illinois, Rep. 244 (1967).
[1103] W. M. McKeeman, ?Grout with equilibration and iteration,? Commun. ACM,5, No. 11, 553?555 (1962). · doi:10.1145/368996.369009
[1104] J. M. McNamee, ?A sparse matrix package. Algorithm 408,? Commun. ACM,14, 265?273 (1971). · Zbl 0522.65024 · doi:10.1145/362575.362584
[1105] M. Meicler, ?A steepest ascent method for the Chebyshev problem,? Math. Comput.,23, No. 108, 813?817 (1969). · Zbl 0208.40605 · doi:10.1090/S0025-5718-1969-0258251-6
[1106] J. Meinguet, ?Sens et protées des arithmétiques de signification,? Colloq. Internat. Centre Nat. Rec. Scient., No. 165, 305?326 (1968).
[1107] J. Meinguet, ?On the estimation of significance,? in: Topic in Interval Analysis, Clarendon Press, Oxford (1969), pp. 47?64.
[1108] N. C. Metropolis, Analysis of Inherent Errors in Matrix Decomposition Using Unnormalized Arithmetic, Proc. IFIP Congr. 65, New York City, 1965, Vol. 2, Sparten Books, Washington; MacMillan, London (1966), pp. 441?442.
[1109] N. C. Metropolis, ?Algorithms in unnormalized arithmetic: polynomial evaluation and matrix decomposition,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 293?303 (1968).
[1110] N. C. Metropolis, ?Analyzed binary computing,? IEEE Trans. Comput.,C-22, No. 6, 573?576 (1973). · Zbl 0258.65048 · doi:10.1109/TC.1973.5009109
[1111] N. C. Metropolis and R. L. Ashenhurst, ?Significant digit computer arithmetic,? IRE Trans. Electron. Comput.,EC-7, No. 4, 265?267 (1958). · doi:10.1109/TEC.1958.5222657
[1112] C. D. Meyer, ?On ranks of pseudoinverses,? SIAM Rev.,11, No. 3, 382?385 (1969). · Zbl 0186.05401 · doi:10.1137/1011062
[1113] C. D. Meyer, ?Generalized inverses of triangular matrices,? SIAM J. Appl. Math.,18, No. 2, 401?406 (1970). · Zbl 0192.36701 · doi:10.1137/0118034
[1114] C. D. Meyer, ?Generalized inverses of block triangular matrices,? SIAM J. Appl. Math.,19, No. 4, 741?750 (1970). · Zbl 0237.15003 · doi:10.1137/0119075
[1115] C. D. Meyer, ?Some remarks on EPr matrices, and generalized inverses,? Linear Algebra Appl.,3, No. 2, 275?278 (1970). · Zbl 0203.33203 · doi:10.1016/0024-3795(70)90020-0
[1116] C. D. Meyer, ?The Moore-Penrose inverse of a bordered matrix,? Linear Algebra Appl.,5, No. 4, 375?382 (1972). · Zbl 0241.15002
[1117] C. D. Meyer, ?Generalized inversion of modified matrices,? SIAM J. Appl. Math.,24, No. 3, 315?323 (1973). · Zbl 0253.15001 · doi:10.1137/0124033
[1118] C. D. Meyer, ?Generalized inverses and ranks of block matrices,? SIAM J. Appl. Math.,25, No. 4, 597?602 (1973). · Zbl 0239.15002 · doi:10.1137/0125057
[1119] C. D. Meyer and R. J. Painter, ?Note on a least squares inverse for a matrix,? J. Assoc. Comput. Mach.,17, No. 1, 110?112 (1970). · Zbl 0206.32002 · doi:10.1145/321556.321566
[1120] J. Miclosko, ?The numerical computation of three-term recurrence relations and the tridiagonal system of linear equations by the method of shooting,? Zh. Vychisl. Mat. Mat. Fiz.,14, No. 6, 1371?1377 (1974). · Zbl 0297.65073
[1121] L. Mihalyffy, ?A note on the matrix inversion by the partitioning technique,? Stud. Sci. Math. Hung.,5, Nos. 1?2, 127?135 (1970). · Zbl 0236.15006
[1122] L. Mihalyffy, ?An alternative representation of the generalized inverse of partitioned matrices,? Linear Algebra Appl.,4, No. 1, 95?100 (1971). · Zbl 0236.15007 · doi:10.1016/0024-3795(71)90031-0
[1123] W. Miller, ?A note on the instability of Gaussian elimination,? BIT,11, No. 4, 422?424 (1971). · Zbl 0231.65033 · doi:10.1007/BF01939411
[1124] W. Miller, ?On an interval-arithmetic matrix method,? BIT,12, No. 2, 213?219 (1972). · Zbl 0242.65034 · doi:10.1007/BF01932816
[1125] W. Miller, ?On the stability of finite numerical procedures,? Numer. Math.,19, No. 5, 425?432 (1972). · doi:10.1007/BF01404925
[1126] R. D. Milne, ?An oblique matrix pseudoinverse,? SIAM J. Appl. Math.,16, No. 5, 931?944 (1968). · Zbl 0167.30304 · doi:10.1137/0116075
[1127] H. W. Milnes, ?A note concerning the properties of a certain class of test matrices,? Math. Comput.,22, No. 104, 827?832 (1968).
[1128] H. W. Milnes and T. S. Chow, ?Note concerning an improved Givens’ method,? Industr. Math.,18, 25?30 (1968).
[1129] P. Mirescu, ?Asupra formei produs a inversii unei baze,? Ann. Univ. Bucuresti. Ser. Sti. Natur. Mat.-Mec.,14, No. 2, 135?141 (1965).
[1130] L. Mirsky, ?Symmetric gauge functions and unitarily invariant norms,? Q. J. Math.,11, No. 41, 50?59 (1960). · Zbl 0105.01101 · doi:10.1093/qmath/11.1.50
[1131] K. D. Misra, ?Monte Carlo methods and possible applications to system problems,? Univ. Roorkee Res. J.,9, Nos. 1?2, Pt. 3, 1?14 (1966).
[1132] I. N. Molchanov and M. F. Iakovlev, ?On one class of iterative methods for obtaining the generalized solution of nonconsistent systems of linear algebraic equations,? Inf. Process. Lett.,2, No. 3, 86?90 (1973). · Zbl 0277.65018 · doi:10.1016/0020-0190(73)90007-0
[1133] I. N. Molchanov and L. D. Nicolenko, ?On an approach to integrating boundary problems with a non-unique solution,? Inf. Process. Lett.,1, 168?172 (1972). · Zbl 0243.65059 · doi:10.1016/0020-0190(72)90052-X
[1134] C. B. Moler, ?Iterative refinement in floating point,? J. Assoc. Comput. Mach.,14, No. 2, 316?321 (1967). · Zbl 0161.35501 · doi:10.1145/321386.321394
[1135] C. B. Moler, Accurate Solution of Linear Algebraic Systems -A Survey, AFIPS Conf. Proc, Vol. 30, Spring Joint Computer Conf., Atlantic City, New Jersey 1967, Thompson Books, Washington, D. C., Academic Press, London (1967), pp. 321?324.
[1136] C. B. Moler, ?Numerical solution of matrix problems,? Digest Rec. Joint Conf. Math. and Comput. Aids Design, Anaheim, California, 1969, New York, New York (1969), pp. 15?26.
[1137] C. B. Moler, ?Matrix computations with Fortran and Paking,? Commun. ACM,15, No. 4, 268?270 (1972). · doi:10.1145/361284.361297
[1138] C. B. Moler and G. W. Stewart, ?An algorithm for generalized matrix eigenvalue problems,? SIAM J. Numer. Anal.,10, No. 2, 241?256 (1973). · Zbl 0253.65019 · doi:10.1137/0710024
[1139] I. N. Moltschanow and M. F. Jakowlew, ?Die Iterations methoden mit Regularisierung nach Samarski zur Lösung einer Aufgabenklasse unverträglicher Systeme linearer algebraischer Gleichungen,? Wiss. Z. Tech. Hochsch. O. Guericke Magdeburg,17, No. 1, 71?75 (1973). · Zbl 0264.65031
[1140] I. N. Moltschanow, W. G. Prikastschikow, and D. S. Subatenko, ?Ein Programmpaket zur Lösung des vollständigen algebraischen Eigenwertproblems,? Wiss. Z. Tech. Hochsch. O. Guericke Magdeburg,17, No. 1, 67?70 (1973).
[1141] E. H. Moore, General Analysis. Part 1, Am. Phil. Soc., Philadelphia (1935), Chap. VII.
[1142] R. E. Moore, ?Interval arithmetic and automatic error analysis in digital computing,? Appl. Math. Statist. Laboratories, Stanford Univ. Tech. Rep., No. 25 (1962).
[1143] R. E. Moore, ?The automatic analysis and control of error in digital computing based on the use of interval numbers,? in: Error in Digital Computation, Vol. 1, Wiley, New York-London-Sydney (1965), pp. 61?130. · Zbl 0202.45002
[1144] R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, New Jersey (1966), Chap. XI. · Zbl 0176.13301
[1145] R. E. Moore, ?Practical aspects of interval computation,? Apl. Mat.,13, No. 1, 52?92 (1968). · Zbl 0184.37401
[1146] R. E. Moore, ?Introduction to algebraic problem,? in: Topic in Interval Analysis, Clarendon Press, Oxford (1969), pp. 3?9.
[1147] P. Morel, ?A propos d’un probleme inverse de valeurs propres,? C. R. Acad. Sci.,277, No. 2, A125-A128 (1973). · Zbl 0262.65028
[1148] G. L. Morris and P. L. Odell, ?A characterization for generalized inverses of matrices,? SIAM Rev.,10, 208?211 (1968). · Zbl 0179.05105 · doi:10.1137/1010032
[1149] D. Moursund, ?Chebyshev solution of n+1 linear equations in n unknowns,? J. Assoc. Comput. Mach.,12, No. 3, 383?387 (1965). · Zbl 0142.11505 · doi:10.1145/321281.321289
[1150] Y. Muda, ?A new relaxation method for obtaining the lowest eigenvalue and eigenvector of a matrix equation,? Int. J. Numer. Meth. Eng.,6, No. 4, 511?519 (1973). · Zbl 0258.65039 · doi:10.1002/nme.1620060407
[1151] D. J. Mueller, ?Householder’s method for complex matrices and eigensystems of hermitian matrices,? Numer. Math.,8, No. 1, 72?92 (1966). · Zbl 0221.65071 · doi:10.1007/BF02165240
[1152] P. H. Müller, ?Eigenwertabschätzungen für Gleichungen vom Typ (?2I ??A ?B)x=0,? Arch. Math.,12, No. 4, 307?310 (1961). · Zbl 0103.08601 · doi:10.1007/BF01650565
[1153] H. Nagasaka, ?Error propagation in the solution of tridiagonal linear equations,? Inf. Process. Jpn.,5, 38?44 (1965). · Zbl 0222.65040
[1154] K. Nakashima, ?On the computation of the general eigenproblem,? Proc. IFIP Congr.62, Munich, 1962, North-Holland, Amsterdam (1963), p. 201. · Zbl 0143.17204
[1155] K. Nakashima, ?On the computation of the general eigenproblem,? Inf. Process, Jpn.,3, 25?32 (1963). · Zbl 0143.17204
[1156] M. Nakhla, K. Singhal, and J. Vlach, ?An optimal pivoting order for the solution of sparse systems of equations,? IEEE Trans. Circuits Syst.,21, No. 2, 222?225 (1974). · doi:10.1109/TCS.1974.1083827
[1157] Kh. Nasitta and M. Gerfeld, ?Iterative Berechnung von Eigenwerten und Eigenvektoren ohne Vorgabe von Näherungen,? Z. Angew. Math. Mech.,51, No. 5, 353?358 (1971). · Zbl 0221.65065 · doi:10.1002/zamm.19710510503
[1158] R. K. Nesbet, ?Algorithm for diagonalization of large matrices,? J. Chem. Phys.,43, No. 1, 311?312 (1965). · doi:10.1063/1.1696477
[1159] J. E. van Ness, ?The inverse iteration method for finding eigenvectors,? 9th Joint Automat. Control. Conf., Ann Arbor, Mich., 1968, Preprints Tech. Papers, New York, New York (1968), pp. 208?209.
[1160] J. E. van Ness, ?Inverse iteration method for finding eigenvectors,? IEEE Trans. Autom. Control.,14, No. 1, 63?66 (1969). · doi:10.1109/TAC.1969.1099097
[1161] A. C. R. Newbery, ?Pei matrix eigenvectors,? Commun. ACM,6, No. 9, 515 (1963). · doi:10.1145/367593.367598
[1162] A. C. R. Newbery, ?A family of test matrices,? Commun. ACM,7, 724 (1964). · Zbl 0126.32104 · doi:10.1145/355588.365131
[1163] M. Newman, ?How to determine the accuracy of the output of a matrix inversion program,? J. Res. Nat. Bur. Stand.,B78, No. 2, 65?68 (1974). · Zbl 0294.65017 · doi:10.6028/jres.078B.009
[1164] N. K. Nichols, ?On the convergence of two-stage iterative processes for solving linear equations,? SIAM J. Numer. Anal.,10, No. 3, 460?469 (1973). · Zbl 0259.65040 · doi:10.1137/0710040
[1165] N. K. Nichols and L. Fox, ?Generalized consistent ordering and the optimum successive overrelaxation factor,? Numer. Math.,13, No. 5, 425?433 (1969). · Zbl 0172.42502 · doi:10.1007/BF02163270
[1166] K. Nickel, ?Triplex-algol application,? in: Topic in Interval Analysis, Clarendon Press, Oxford (1969), pp. 10?24.
[1167] R. A. Nicolaides, ?On a geometrical aspect of SOR and the theory of consistent ordering for positive-definite matrices,? Numer. Math.,23, No. 2, 99?104 (1974). · doi:10.1007/BF01459944
[1168] W. Niethammer, ?Relaxation bei nichtsymmetrischen Matrizen,? Math. Z.,85, No. 4, 319?327 (1964). · Zbl 0246.65015 · doi:10.1007/BF01110678
[1169] W. Niethammer, ?Relaxation bei komplexen Matrizen,? Math. Z.,86, No. 1, 34?40 (1964). · Zbl 0242.65036 · doi:10.1007/BF01111275
[1170] W. Niethammer, ?Überrelaxation bei linearen Gleichungssystemen mit schiefsymmetrischer Koeffi-zientenmatrix,? Inaug.-Diss., Tübingen, Eberhard-Karls-Univ. (1964).
[1171] W. Niethammer, ?Relaxation bei Matrizen mit der Eigenschaft ?A?,? Z. Angew. Math. Mech.,44, Sonderh., T49-T52 (1964). · Zbl 0137.33001
[1172] W. Niethammer, ?Iterationsverfahren und algemeine Euler-Verfahren,? Math. Z.,102, No. 4, 288?317 (1967). · Zbl 0225.65008 · doi:10.1007/BF01110911
[1173] W. Niethammer, ?Über- und Unterrelaxation bei linearen Gleichungssystemen,? Computing,5, No. 3, 303?311 (1970). · Zbl 0209.46702 · doi:10.1007/BF02248030
[1174] W. Niethammer, ?Konvergenzbereiche bei mehrstufigen Iterationsverfahren,? Z. Angew. Math. Mech.,50, Sonderh. 1?4, T70-T72 (1970). · Zbl 0203.47903 · doi:10.1002/zamm.19700500131
[1175] W. Niethammer, ?Konvergenzbeschleunigung bei einstufigen Iterationsverfahren durch Summierungs-methoden, Iterationsverfahren,? Numer. Math. Approx.-teor., Sonderdruck Aus,15, 235?243 (1970).
[1176] R. M. Nisbet, ?Acceleration of the convergence in Nesbet’s algorithm for eigenvalues and eigenvectors of large matrices,? J. Comput. Phys.,10, No. 3, 614?619 (1972). · Zbl 0247.65026 · doi:10.1016/0021-9991(72)90055-1
[1177] Ben Noble, ?A method for computing the generalized inverse of a matrix,? SIAM J. Numer. Anal.,3, No. 4, 582?584 (1966). · Zbl 0147.13105 · doi:10.1137/0703049
[1178] Ph. Noel, ?Une methode de résolution des grands systèmes linéaires par suritération polynomiale. I,? Bul. Inst. Politechn. Iasi,13, Nos. 3?4, 119?122 (1967).
[1179] Ph. Noel, ?Une méthode de résolution des grands systemes linéaires par suriteration polynomiale. II,? Bul. Inst. Politechn. Iasi,14, Nos. 1?2, 111?114 (1968).
[1180] L. Nolin, ?Sur l’élimination d’une valeur propre dans une matrice tridiagonale,? C. R. Acad. Sci.,256, No. 9, 1904?1907 (1963). · Zbl 0118.25804
[1181] M. Novakova, ?Loss of significant figures during the multiplication of approximative values,? Stroje Zpracov. Inf., No. 12, 265?274 (1966).
[1182] E. Nuding and I. Kahlert-Warmbold, ?A computer-oriented representation of matrices,? Computing,6, Nos. 1?2, 1?8 (1970). · Zbl 0212.16902 · doi:10.1007/BF02241728
[1183] E. Nuding, I. Warmbold, H. -P. Wolf, and B. Ehret, ?Matrizen höher Ordnung mit ausgezeichneter Struktur,? Z. Angew. Math. Mech.,46, Sonderh., T74-T76 (1966).
[1184] E. Nuding and J. Wilhelm, ?Über Gleichungen und über Lösungen,? Z. Angew. Math. Mech.,52, No. 4, 188?190 (1972). · Zbl 0236.65032
[1185] M. J. O’Carroll, ?Inconsistencies and S. O. R. convergence for the discrete Neumann problem,? J. Inst. Math. Appl.,11, No. 3, 343?350 (1973). · Zbl 0258.65103 · doi:10.1093/imamat/11.3.343
[1186] W. Oettli, ?On the solution set of a linear system with inaccurate coefficients,? SIAM J. Numer. Anal.,2, No. 1, 115?118 (1965). · Zbl 0146.13404
[1187] W. Oettli and W. Prager, ?Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides,? Numer. Math.,6, No. 5, 405?409 (1964). · Zbl 0133.08603 · doi:10.1007/BF01386090
[1188] W. Oettli, W. Prager, and J. H. Wilkinson, ?Admissible solutions of linear systems with not sharply defined coefficients,? SIAM J. Numer. Anal.,2, No. 2, 291?299 (1965). · Zbl 0154.16903
[1189] E. C. Ogbuobiri, W. F. Tinney, and J. W. Walker, ?Sparsity directed decomposition for Gaussian elimination of matrices,? IEEE Trans. Power Apparatus Systems PAS89, 141?155 (1970). · doi:10.1109/TPAS.1970.292682
[1190] T. A. Oliphant, ?An extrapolation procedure for solving linear systems,? Q. Appl. Math.,20, 257?265 (1962). · Zbl 0109.34601 · doi:10.1090/qam/143350
[1191] T. A. Oliphant, ?A note on extrapolation procedures for solving linear systems,? Q. Appl. Math.,21, No. 1, 72?75 (1963). · Zbl 0112.07603 · doi:10.1090/qam/144456
[1192] G. N. de Oliveira, ?Note on the additive inverse eigenvalue problem,? Rev. Fac. Cienc. Univ. Lisboa,A-13, No. 1, 21?26 (1969?1970).
[1193] G. N. de Oliveira, ?Inverse eigenvalue problems for complex matrices,? Computing,6, Nos. 3?4, 339?341 (1970). · Zbl 0221.15008 · doi:10.1007/BF02238818
[1194] G. N. de Oliveira, ?Note on an inverse characteristic value problem,? Numer. Math.,15, No. 4, 345?347 (1970). · Zbl 0202.03504 · doi:10.1007/BF02165126
[1195] G. N. de Oliveira, ?Matrix inequalities and the additive inverse eigenvalue problem,? Computing,9, No. 2, 95?100 (1972). · Zbl 0247.15007 · doi:10.1007/BF02236959
[1196] G. N. de Oliveira, ?On the multiplicative inverse eigenvalue problem,? Can. Math. Bull.,15, No. 2, 189?193 (1972). · Zbl 0247.15006 · doi:10.4153/CMB-1972-034-0
[1197] Gh. Olteanu, ?Sur l’inversion des matrices bandes,? Bul. Sti. Inst. Constr. Bucuresti,14, No. 3, 299?305 (1971).
[1198] W. Orchard-Hays, ?MP systems technology for large sparse matrices,? in: Sparse Matrix Proceedings, R. A. Willoughby (ed.), RA 1, No. 11707, IBM Corp. Thomas J. Watson Res. Center, Yorktown Heights, New York (1969), Chap. XXII, pp. 59?64.
[1199] J. M. Ortega, ?An error analysis of Householder’s method for the symmetric eigenvalue problem,? Numer. Math.,5, No. 3, 211?225 (1963). · Zbl 0115.34501 · doi:10.1007/BF01385892
[1200] J. M. Ortega, ?Generation of test matrices by similarity transformations,? Commun. ACM,7, No. 6, 377?378 (1964). · Zbl 0126.32103 · doi:10.1145/512274.512293
[1201] J. M. Ortega and H. F. Kaiser, ?The LLT and QR methods for symmetric tridiagonal matrices,? Comput. J.,6, No. 1, 99?101 (1963). · Zbl 0113.32005 · doi:10.1093/comjnl/6.1.99
[1202] E. E. Osborne, ?Smallest least squares solutions of linear equations,? SIAM J. Numer. Anal.,2, No. 2, 300?307 (1965). · Zbl 0142.11602
[1203] M. R. Osborne, ?A new method for the solution of eigenvalue problems,? Comput. J.,7, No. 3, 228?232 (1964). · Zbl 0208.18204 · doi:10.1093/comjnl/7.3.228
[1204] M. R. Osborne, ?On the inverse eigenvalue problem for matrices and related problems for difference an and differential equations,? Lect. Notes Math.,228, 155?168 (1971). · Zbl 0238.65015 · doi:10.1007/BFb0069454
[1205] M. R. Osborne and S. Michaelson, ?The numerical solution of eigenvalue problems inwhich the eigenvalue parameter appears nonlinearly, with an application to differential equations,? Comput. J.,7, No. 1, 66?71 (1964). · Zbl 0221.65131 · doi:10.1093/comjnl/7.1.66
[1206] A. M. Ostrowski, ?On some metrical properties of operator matrices and matrices partitioned into blocks,? J. Math. Anal. Appl.,2, No. 2, 161?209 (1961). · Zbl 0101.25504 · doi:10.1016/0022-247X(61)90030-0
[1207] A. M. Ostrowski, ?Iterative solution of linear systems of functional equations,? J. Math. Anal. Appl.,2, No. 3, 351?369 (1961). · Zbl 0100.33305 · doi:10.1016/0022-247X(61)90016-6
[1208] A. M. Ostrowski, Solution of Equations and Systems of Equations, 2nd ed., Academic Press, New York-London (1966), Chap. XIV. · Zbl 0222.65070
[1209] A. M. Ostrowski, ?Les estimations des erreurs à postériori dans les procédés itératifs,? C. R. Acad. Sci.,275, No. 4, A275-A278 (1972). · Zbl 0237.65041
[1210] A. M. Ostrowski, ?A posteriori error estimates in iterative procedures,? SIAM J. Numer. Anal.,10, No. 2, 290?298 (1973). · Zbl 0263.65058 · doi:10.1137/0710028
[1211] M. H. C. Paardekooper, ?An eigenvalue algorithm based on norm-reducing transformations,? Doct. Diss. Eindhoven Inst. Tech., Eindhoven, Tech. Hogesch. (1969). · Zbl 0207.15604
[1212] M. H. C. Paardekooper, ?Jacobi-methoden voor het numbriek oplossen van het algebraisch eigenwaarde probleem,? Informatie,13, No. 9, 412?419 (1971).
[1213] M. H. C. Paardekooper, ?An eigenvalue algorithm for skew-symmetric matrices,? Numer. Math.,17, No. 3, 189?202 (1971). · Zbl 0228.65031 · doi:10.1007/BF01436375
[1214] C. C. Paige, ?Error analysis of the symmetric Lanczos process for the eigenproblem,? London Univ., Inst. Comput. Sci. Tech., Note ICSI, 209 (1969).
[1215] C. C. Paige, ?Practical use of the symmetric Lanczos process with reorthogonalization,? BIT,10, No. 2, 183?195 (1970). · Zbl 0214.41003 · doi:10.1007/BF01936866
[1216] C. C. Paige, ?The computation of eigenvalues and eigenvectors of very large sparse matrices,? Diss. London Univ. Inst. Comput. Sci. (1971).
[1217] C. C. Paige, ?Computational variants of the Lanczos method for the eigenproblem,? J. Inst. Math. Appl.,10, No. 3, 373?381 (1972). · Zbl 0253.65020 · doi:10.1093/imamat/10.3.373
[1218] C. C. Paige, ?An error analysis of a method for solving matrix equations,? Math. Comput.,27, No. 122, 355?359 (1973). · Zbl 0282.65027 · doi:10.1090/S0025-5718-1973-0331745-1
[1219] C. C. Paige, ?Bidiagonalization of matrices and solution of linear equations,? SIAM J. Numer. Anal.,11, No. 1, 197?209 (1974). · Zbl 0244.65023 · doi:10.1137/0711019
[1220] C. C. Paige, ?Eigenvalues of perturbed Hermit Lanmatrices,? Linear Algebra Appl.,8, No. 1, 1?10 (1974). · Zbl 0275.65011 · doi:10.1016/0024-3795(74)90002-0
[1221] C. C. Paige and M. A. Saunders, ?Solution of sparse indefinite systems of equations and least squares problems,? Rep. Stanford Univ., 65-73-399 (1973).
[1222] C. V. Pao, ?Logarithmic derivatives of a square matrix,? Linear Algebra Appl.,6, 159?164 (1973). · Zbl 0246.15021 · doi:10.1016/0024-3795(73)90015-3
[1223] C. V. Pao, ?A further remark on the logarithmic derivatives of a square matrix,? Linear Algebra Appl.,7, No. 3, 275?278 (1973). · Zbl 0257.15016 · doi:10.1016/0024-3795(73)90044-X
[1224] B. N. Parlett, ?The development and use of methods of LR type,? SIAM Rev.,6, No. 3, 275?295 (1964). · Zbl 0242.65039 · doi:10.1137/1006066
[1225] B. N. Parlett, ?Laguerre’s method applied to the matrix eigenvalue problem,? Math. Comput.,18, No. 87, 464?485 (1964).
[1226] B. N. Parlett, ?A note on LaBudde’s algorithm,? Math. Comput.,18, No. 87, 505?506 (1964).
[1227] B. N. Parlett, ?Convergence of the QR algorithm,? Numer. Math.,7, No. 2, 187?193 (1965). · Zbl 0132.36301 · doi:10.1007/BF01397692
[1228] B. N. Parlett, ?Matrix eigenvalue problems,? Am. Math. Mon.,72, No. 2, Pt. 2, 59?66 (1965). · Zbl 0123.11302 · doi:10.2307/2313311
[1229] B. N. Parlett, ?Singular and invariant matrices under the QR transformation,? Math. Comput.,20, No. 96, 611?615 (1966). · Zbl 0238.65018
[1230] B. N. Parlett, ?Necessary and sufficient conditions for convergence of the QR algorithm on Hessenberg matrices,? Proc. Assoc. Comput. Mach. Nat. MTG, 14?19 (1966).
[1231] B. N. Parlett, ?The LU and QR algorithms,? in: Math. Methods for Digital Computers, Vol. 2, 2nd ed., Wiley, New York-London-Sydney (1967), pp. 116?130.
[1232] B. N. Parlett, ?Global convergence of the basic QR algorithm on Hessenberg matrices,? Math. Comput.,22, No. 104, 803?817 (1968). · Zbl 0184.37602
[1233] B. N. Parlett, ?Analysis of algorithms for reflections in bisectors,? SIAM Rev.,13, No. 2, 197?208 (1971). · Zbl 0217.52606 · doi:10.1137/1013037
[1234] B. N. Parlett, ?Certain matrix eigenvalue techniques discussed from a geometric point of view,? U. K. Atom. Energy Auth. Res. Group, NAERE-R 7168 (1973).
[1235] B. N. Parlett, ?Présentation géométrique des methodes de calcul des valeurs propres,? Numer. Math.,21, No. 3, 223?233 (1973). · Zbl 0255.65020 · doi:10.1007/BF01436626
[1236] B. N. Parlett, ?Normal Hessenberg and moment matrices,? Linear Algebra Appl.,6, 37?43 (1973). · Zbl 0251.15022 · doi:10.1016/0024-3795(73)90005-0
[1237] B. N. Parlett, ?The Rayleigh quotient iteration and some generalization for nonnormal matrices,? Math. Comput.,28, No. 127, 679?693 (1974). · Zbl 0293.65023 · doi:10.1090/S0025-5718-1974-0405823-3
[1238] B. N. Parlett and W. Kahan, ?On the convergence of a practical QR algorithm,? Proc. IFIP Congr. 68, Edinburgh, 1968, Vol. I: Mathematics, Software, North-Holland, Amsterdam (1969), pp. 114?118. · Zbl 0195.45002
[1239] B. N. Parlett and W. G. Poole, ?A geometric theory for the QR, LU and power iterations,? SIAM J. Numer. Anal.,10, No. 2, 389?412 (1973). · Zbl 0253.65018 · doi:10.1137/0710035
[1240] B. N. Parlett and J. K. Reid, ?On the solution of a system of linear equations whose matrix is symmetric but not definite,? BIT,10, No. 3, 386?397 (1970).
[1241] B. N. Parlett and C. Reinsch, ?Balancing a matrix for calculation of eigenvalues and eigenvectors,? Numer. Math.,13, No. 4, 293?304 (1969). · Zbl 0184.37703 · doi:10.1007/BF02165404
[1242] Kl. Pasedach, ?Zur Konvergenz der Eigenvektoren beim Jacobi-Verfahren,? Z. Angew. Math. Mech.,46, Nos. 3?4, 197?200 (1966). · Zbl 0222.65045 · doi:10.1002/zamm.19660460306
[1243] P. C. Patton, ?Quelques algorithmes récents adaptés aux ensembles électroniques pour le calcul des valeurs propres d’une matrice,? Rev. Frac. Mec., No. 13, 21?23 (1965).
[1244] P. C. Patton, ?Die simultane Berechnung von Eigenvektoren und Eigenwertspektren beliebiger dynamischer Matrizen,? Stuttgar., Tech. Hochsch. (1966).
[1245] G. Patzelt, ?Fehleruntersuchungen bei der Lösung linearer Gleichungssysteme durch elektronische Digitalrechner,? Z. Angew. Math. Mech.,41, Sonderh., T50-T52 (1961). · Zbl 0104.09901
[1246] C. Pearcy, ?On convergence of alternating direction procedures,? Numer. Math.,4, No. 2, 172?176 (1962). · Zbl 0112.34802 · doi:10.1007/BF01386310
[1247] M. H. Pearl, ?On normal and EPr matrices,? Mich. Math. J.,6, 1?5 (1959). · Zbl 0084.01702 · doi:10.1307/mmj/1028998132
[1248] M. H. Pearl, ?On normal EPr matrices,? Mich. Math. J.,8, No. 1, 33?37 (1961). · Zbl 0103.00903 · doi:10.1307/mmj/1028998512
[1249] M. C. Pease, ?Matrix inversion using parallel processing,? J. Assoc. Comput. Mach.,14, No. 4, 757?764 (1967). · Zbl 0171.15302 · doi:10.1145/321420.321434
[1250] M. C. Pease, ?Inversion of matrices by partitioning,? J. Assoc. Comput. Mach.,16, No. 2, 302?314 (1969). · Zbl 0202.15303 · doi:10.1145/321510.321522
[1251] M. I. Pei, ?A test matrix for inversion procedures,? Commun. ACM,5, No. 10, 508 (1962). · doi:10.1145/368959.368975
[1252] R. Penrose, ?A generalized inverse for matrices,? Proc. Cambridge Phil. Soc.,51, No. 3, 406?413 (1955). · Zbl 0065.24603 · doi:10.1017/S0305004100030401
[1253] V. Pereyra, ?Stabilizing linear least squares problems,? Proc. IFIP Congr. 68, Edinburgh, 1968, Vol. 1: Mathematics, Software, North-Holland, Amsterdam (1969), pp. 119?121.
[1254] V. Pereyra, ?Stability of general systems of linear equations,? Aequat. Math.,2, Nos. 2?3, 194?206 (1969). · Zbl 0172.42501 · doi:10.1007/BF01817705
[1255] V. Pereyra and J. B. Posen, ?Computation of the pseudoinverse of a matrix of unknown rank,? Computer Sci. Dept. Stanford Univ., Tech. Rep., CS13 (1964).
[1256] V. Pereyra and G. Scherer, ?Eigenvalues of symmetric tridiagonal matrices: a fast, accurate, and reliable algorithm,? J. Inst. Math. Appl.,12, No. 2, 209?222 (1973). · Zbl 0278.65035 · doi:10.1093/imamat/12.2.209
[1257] G. Peters and J. H. Wilkinson, ?Eigenvalues of Ax=?Bx with band symmetric A and B,? Comput. J.,12, No. 4, 398?404 (1969). · Zbl 0185.40204 · doi:10.1093/comjnl/12.4.398
[1258] G. Peters and J. H. Wilkinson, ?Ax=?Bx and the generalized eigenproblem,? SIAM J. Numer. Anal.,7, No. 4, 479?492 (1970). · Zbl 0276.15016 · doi:10.1137/0707039
[1259] G. Peters and J. H. Wilkinson, ?The least squares problem and pseudoinverses,? Comput. J.,13, No. 3, 309?316 (1970). · Zbl 0195.44804 · doi:10.1093/comjnl/13.3.309
[1260] G. Peters and J. H. Wilkinson, ?Eigenvectors of real and complex matrices by LR and QR triangularizations,? Numer. Math.,113, No. 3, 181?204 (1970). · Zbl 0208.18303 · doi:10.1007/BF02219772
[1261] G. Peters and J. H. Wilkinson, ?The calculation of specified eigenvectors by inverse iteration,? Grundlehren Math. Wiss. Einzeldarstell.,186, 418?439 (1971).
[1262] W. V. Petryshyn, ?The generalized overrelaxation method for the approximate solution of operator equations in Hubert space,? SIAM J. Appl. Math.,10, No. 4, 675?690 (1962). · Zbl 0106.31804 · doi:10.1137/0110052
[1263] W. V. Petryshyn, ?On a general iterative method for the approximate solution of linear operator equations,? Math. Comput.,17, No. 81, 1?10 (1963). · Zbl 0111.31701 · doi:10.1090/S0025-5718-1963-0163426-5
[1264] W. V. Petryshyn, ?On the generalized overrelaxation method for operator equations,? Proc. Am. Math. Soc.,14, No. 6, 917?924 (1963). · Zbl 0128.11602 · doi:10.1090/S0002-9939-1963-0169402-2
[1265] W. V. Petryshyn, ?On the extrapolated Jacobi or simultaneous displacements method in the solution of matrix and operator equations,? Math. Comput.,19, No. 89, 37?55 (1965). · Zbl 0131.33801 · doi:10.1090/S0025-5718-1965-0176601-2
[1266] W. V. Petryshyn, ?On generalized inverses and on the uniform convergence of (I-BKn) with application to iterative methods,? J. Math. Anal. Appl.,18, No. 3, 417?439 (1967). · Zbl 0189.47502 · doi:10.1016/0022-247X(67)90036-4
[1267] D. Pham, Techniques du Calcul Matriciel, Dunod, Paris (1962), Chap. XIII.
[1268] J. L. Phillips, ?The triangular decomposition of Hankel matrices,? Math. Comput.,25, No. 115, 599?602 (1971). · Zbl 0222.65053 · doi:10.2307/2005223
[1269] J. B. Plant, ?An algorithm for approximately diagonalizing a matrix,? Proc. IEEE,57, No. 2, 239?241 (1969). · doi:10.1109/PROC.1969.6941
[1270] R. J. Plemmons, ?Monotonicity and iterative approximations involving rectangular matrices,? Math. Comput.,26, No. 120, 853?858 (1972). · Zbl 0263.65046 · doi:10.1090/S0025-5718-1972-0315882-2
[1271] R. J. Plemmons, ?Linear least squares by elimination and MGS,? J. Assoc. Comput. Mach.,21, No. 4, 581?585 (1974). · Zbl 0289.65019 · doi:10.1145/321850.321855
[1272] R. J. Plemmons and R. E. Cline, ?The generalized inverse of a nonnegative matrix,? Proc. Am. Math. Soc.,31, No. 1, 46?50 (1972). · Zbl 0241.15001 · doi:10.1090/S0002-9939-1972-0285541-5
[1273] O. Pokorna, ?A method of inverting matrices,? Apl. Mat.,15, No. 1, 1?9 (1970). · Zbl 0194.18101
[1274] P. Poliak, M. Postulkova, and R. Vyhnanska, ?Solution of linear algebraic equations with three-diagonal ill-conditioned system matrix,? Apl. Mat.,15, No. 4, 227?234 (1970). · Zbl 0195.44904
[1275] G. D. Poole and T. L. Boullion, ?Weak spectral inverses which are partial isometries,? SIAM J. Appl. Math.,23, 171?172 (1972). · Zbl 0247.15003 · doi:10.1137/0123018
[1276] W. G. Poole, ?A geometric convergence theory for the QR, Rayleigh quotient, and power iteration,? Comput. Center, Univ. California, Berkeley, Tech. Rep. 41 (1970).
[1277] C. Gh. Popa, ?Nota asupra inversarii matricilor singulare,? Lucrarile ?tiint. Inst. Pedagog. Timi?oara Mat.-Fiz., 149?153 (1962).
[1278] A. J. Pope, ?An algorithm for the pseudoinverse of sparse matrices,? NCAA, Geodetic Research Lab., Rockville, Maryland (1972).
[1279] M. J. D. Powell, ?A theorem on rank one modifications to a matrix and its inverse,? Comput. J.,12, No. 3, 288?290 (1969). · Zbl 0182.48904 · doi:10.1093/comjnl/12.3.288
[1280] M. J. D. Powell and J. K. Reid, ?On applying Householder transformations to linear least squares problems,? Proc. IFIP Congr. 68, Edinburgh, 1968, Vol. 1: Mathematics, Software, North-Holland, Amsterdam (1969), pp. 122?126.
[1281] H. S. Price and R. S. Varga, ?Recent numerical experiments comparing successive overrelaxation iterative methods with alternating direction implicit methods,? Gulf Research and Development Co., Research Project No. 84-1-40, Reservoir Mechanics Division, Rep. No. 91 (1962).
[1282] R. L. Probert, ?On the complexity of symmetric computations,? INFOR. Can. J. Oper. Res. Inf. Process.,12, No. 1, 71?86 (1974). · Zbl 0277.68022
[1283] P. Pulay, ?An iterative method for the determination of the square root of a positive-definite matrix,? Z. Angew. Math. Mech.,46, No. 2, 151 (1966). · Zbl 0151.21302 · doi:10.1002/zamm.19660460214
[1284] L. D. Pyle, ?Generalized inverse computations using the gradient projection method,? J. Assoc. Comput. Mach.,11, No. 4, 422?428 (1964). · Zbl 0123.11203 · doi:10.1145/321239.321243
[1285] L. D. Pyle, ?A generalized inverse e-algorithm for constructing intersection projection matrices, with applications,? Numer. Math.,10, No. 1, 86?102 (1967). · Zbl 0152.14703 · doi:10.1007/BF02165164
[1286] L. D. Pyle, ?Remarks on a generalized inverse e-algorithm for matrices,? Proc. Symp. on Theory and Appl. of Generalized Inverses of Matrices, Texas Tech. College, Lubbock, Texas (1968), pp. 218?238. · Zbl 0187.40001
[1287] M. Radic, ?On a generalization of the Arghiriade-Dragomir representation of the Moore -Penrose inverse,? Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis., Mat. e Natur.,44, No. 3, 333?336 (1968). · Zbl 0185.07702
[1288] J. W. Rainey, ?On comparatively stable tridiagonalization methods,? Numer. Math.,13, No. 4, 316?322 (1969). · Zbl 0179.21404 · doi:10.1007/BF02165406
[1289] J. W. Rainey and G. J. Habetler, ?An application of the LR factorization to sequential tridiagonalization methods,? SIAM J. Appl. Math.,17, No. 1, 212?221 (1969). · Zbl 0194.46801 · doi:10.1137/0117021
[1290] J. W. Rainey and G. J. Habetler, ?Tridiagonalization of completely nonnegative matrices,? Math. Comput.,26, No. 117, 121?128 (1972). · Zbl 0269.65024 · doi:10.1090/S0025-5718-1972-0309290-8
[1291] C. R. Rao, ?Calculus of generalized inverses of matrices. Part I. General theory,? Sankhya,29, No. 3, 317?342 (1967).
[1292] C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and Its Applications, Wiley, New York-London-Sydney-Toronto (1971), Chap. IX. · Zbl 0236.15004
[1293] C. R. Rao and S. K. Mitra, ?Theory and application of constrained inverse of matrices,? SIAM J. Appl. Math.,24, No. 4, 473?488 (1973). · Zbl 0237.15001 · doi:10.1137/0124050
[1294] C. R. Rao, S. K. Mitra, and P. Bhimasankaran, ?Determination of matrix by its subclasses of generalized inverses,? Sankhya A,34, 5?8 (1972).
[1295] J. V. V. Rao, ?Some more representation for the generalized inverse of a partitioned matrix,? SIAM J. Appl. Math.,24, No. 2, 272?276 (1973). · Zbl 0251.15006 · doi:10.1137/0124050
[1296] W. D. Ray, ?The inverse of a finite’ Toeplitz matrix,? Technometrics,12, No. 1, 153?156 (1970). · Zbl 0194.34002 · doi:10.1080/00401706.1970.10488643
[1297] L. Rehnqvist, ?Inversion of certain symmetric band matrices,? BIT,12, No. 1, 90?98 (1972). · Zbl 0234.65037 · doi:10.1007/BF01932677
[1298] S. Reich, ?On Aitken’s delta-squared method,? Am. Math. Mon.,77, No. 3, 283?284 (1970). · Zbl 0191.16201 · doi:10.2307/2317712
[1299] J. K. Reid, ?A method for finding the optimum successive overrelaxation parameter,? Comput. J.,9, No. 2, 200?204 (1966). · Zbl 0202.43404 · doi:10.1093/comjnl/9.2.200
[1300] J. K. Reid, ?A note on the least-squares solution of a band system of linear equations by Householder reductions,? Comput. J.,10, No. 2, 188?189 (1967). · Zbl 0168.13305 · doi:10.1093/comjnl/10.2.188
[1301] J. K. Reid, ?A Fortran subroutine for the solution of large sparse sets of linear equations by conjugate gradients,? Res. Group, U.K.Atom. Energy Auth., No. AERE-R (1970).
[1302] J. K. Reid, ?On the method of conjugate gradients for the solution of large sparse systems of linear equations,? in: Large Space Sets of Linear Equations, Academic Press, London-New York (1971), pp. 231?252.
[1303] J. K. Reid, ?A note on the stability of Gaussian elimination,? J. Inst. Math. Appl.,8, No. 3, 374?375 (1971). · Zbl 0229.65030 · doi:10.1093/imamat/8.3.374
[1304] J. K. Reid (ed.), Large Sparse Sets of Linear Equations, Proc. Oxford Conf. Inst. Math. Appl., April 1971, Academic Press, London-New York (1971).
[1305] J. K. Reid, ?The use of conjugate gradients for systems of linear equations possessing ?property A?,? SIAM J. Numer. Anal.,9, No. 2, 325?332 (1972). · Zbl 0259.65037 · doi:10.1137/0709032
[1306] J. K. Reid, ?A discussion on a modified conjugate gradient method. Discussion on the paper: ?Note on a modified conjugate gradient method? by W. L. Wood,? Int. J. Numer. Meth. Eng.,8, No. 2, 431?432 (1974). · doi:10.1002/nme.1620080221
[1307] Ch. H. Reinsch, ?A stable, rational QR algorithm for the computation of the eigenvalues of an Hermitian, tridiagonal matrix,? Math. Comput.,25, No. 115, 591?597 (1971). · Zbl 0222.65044 · doi:10.1090/S0025-5718-1971-0295555-4
[1308] C. Reinsch and F. L. Bauer, ?Rational QR transformation with Newton shift for symmetric tridiagonal matrices,? Numer. Math.,11, No. 3, 264?272 (1968). · Zbl 0164.45201 · doi:10.1007/BF02161847
[1309] T. Relia, ?Über den absoluten Betrag von Matrizen,? Comptes Rendus du Congr. Internat, des Mathematiciens (Oslo, 1936), T. II. Conferences de Sections, Oslo, 29?31 (1937).
[1310] J. Replogle, B. D. Holcomb, and W. R. Burrus, ?The use of mathematical programming for solving singular and poorly conditioned systems of equations,? J. Math. Anal. Appl.,20, No. 2, 310?324 (1967). · Zbl 0166.41505 · doi:10.1016/0022-247X(67)90092-3
[1311] J. R. Rice, ?A theory of condition,? SIAM J. Numer. Anal.,3, No. 2, 287?310 (1966). · Zbl 0143.37101 · doi:10.1137/0703023
[1312] J. R. Rice, ?Experiments on Gram-Schmidt orthogonalization,? Math. Comput.,20, No. 94, 325?328 (1966). · doi:10.1090/S0025-5718-1966-0192673-4
[1313] W. R. Richert, ?Eine Fehlerabschätzung für Eigenwertaufgaben vom Typ (?2I ? ?A ? B)x=0,? Z. Angew. Math. Mech.,53, No. 4, T206 (1973). · Zbl 0262.65082
[1314] R. Richter, ?Probleme bei der Inversion von Matrizen,? Wiss. Z. Hochsch. Verkehrswesen, Dresden,13, No. 3, 339?341 (1966). · Zbl 0173.17804
[1315] R. D. Riess, ?Introduction of a conditioning parameter in computing characteristic equations,? Proc. IEEE,59, No. 8, 1275?1276 (1971). · doi:10.1109/PROC.1971.8392
[1316] J.-L. Rigal, ?Evaluation de la plux courte distance d’une matrice carrée au lieu des matrices singuliéres. Application à l’inversion d’une matrice. II. Distances non euclidiennes,? C. R. Acad. Sci.,252, No. 5, 665?667 (1961).
[1317] J.-L. Rigal, ?Nombre de conditions et de signification en analyse matricielle,? 2-e Congr. Assoc. Franç. Calcul et Traitem. Inform. AFCALTI, Paris, 1961, Gauthier-Villars, Paris (1962), pp. 47?53.
[1318] J.-L. Rigal, ?Problèmes de stabilité concernant les problèmes aux valeurs propres et les polynômes,? 4-e Congr. Calcul et Trailern. Inform. A FIRO, Versailles 1964, Paris (1965), pp. 207?218.
[1319] J. -L. Rigal and J. Gaches, ?On the compatibility of a given solution with the data of a linear system,? J. Assoc. Comput. Mach.,14, No. 3, 543?548 (1967). · Zbl 0183.17704 · doi:10.1145/321406.321416
[1320] J. -L. Rigal and J. F. Maitre, ?Une methode d’inversion partielle avec choix du pivot maximal,? 3-e Congr. Calcul et Traitem. Inform. AFCALTI, Toulouse, 1963, Paris (1965), pp. 157?163.
[1321] A. K. Rigler, ?Estimation of the successive overrelaxation factor,? Math. Comput.,19, No. 90, 302?307 (1965). · Zbl 0131.14202 · doi:10.1090/S0025-5718-1965-0181122-7
[1322] A. K. Rigler, ?A choice of starting vectors in relaxation methods,? J. Comput. Phys.,4, No. 3, 419?423 (1969). · Zbl 0213.16305 · doi:10.1016/0021-9991(69)90009-6
[1323] J. Rissanen, ?Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with application to factoring positive matrix polynomials,? Math. Comput.,27, No. 121, 147?154 (1973). · Zbl 0252.65029 · doi:10.1090/S0025-5718-1973-0329235-5
[1324] J. Rissanen, ?Solution of linear equations with Hankel and Toeplitz matrices,? Numer. Math.,22, No. 5, 361?366 (1974). · Zbl 0272.65021 · doi:10.1007/BF01436919
[1325] T. J. Rivlin, ?Overdetermined systems of linear equations,? SIAM Rev.,5, No. 1, 52?66 (1963). · Zbl 0115.27704 · doi:10.1137/1005005
[1326] F. Robert, ?Normes vectorielles de vecteurs et de matrices,? Rev. Franc. Traitement Inf. Chiffres,7, 261?299 (1964). · Zbl 0242.65044
[1327] F. Robert, ?Sur les normes vectorielles régulières sur un espace vectoriel de dimension finie,? C. R. Acad. Sci.,260, No. 20, A5173-A5176 (1965). · Zbl 0196.29802
[1328] F. Robert, ?Calcul de rapport maximal de deux normes sur Rn,? Rev. Franc. Inf. Rech. Oper.,1, No. 5, 97?118 (1967).
[1329] F. Robert, ?Une ?distance? entre deux matrices A et B, fonction simple du conditionnement de A?1B,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 119?122 (1968).
[1330] F. Robert, ?Etude et utilisation de normes vectorielles en analyse numérique linéaire,? These Doct. Sci. Math. Fac. Sci. Univ. Grenoble (1968).
[1331] F. Robert, ?Block H-matrices et convergence des méthodes iteratives classiques par blocs,? Linear Algebra Appl.,2, 223?265 (1969). · Zbl 0182.21302 · doi:10.1016/0024-3795(69)90029-9
[1332] F. Robert, ?Sur une notion de contraction faible relativement a une norme vectorielle,? C. R. Acad. Sci.,271, No. 2, A96-A99 (1970). · Zbl 0203.47801
[1333] F. Robert, ?Méthodes itératives ?série parallele?,? C. R. Acad. Sci.,271, No. 17, A847-A850 (1970).
[1334] F. Robert, ?Algorithmes tronques de decoupe lineaire,? Rev. Franc. Automat., Inf. Rech. Oper.,6, No. R-2, 45?64 (1972). · Zbl 0246.65014
[1335] F. Robert and J. F. Maitre, ?Normes et algorithmes associés à une découpe de matrice,? C. R. Acad. Sci.,274, No. 8, A644-A647 (1972). · Zbl 0236.15017
[1336] F. Robert and J. F. Maitre, ?Normes et algorithmes associés à une découpe de matrice (iteration du principe de Gauss-Seidel),? Numer. Math.,19, No. 4, 303?325 (1972). · Zbl 0227.65023 · doi:10.1007/BF01404878
[1337] M. L. Rockoff, ?Comparison of some iterative methods for solving large systems of linear equations,? Doct. Diss. Univ. Pa. (1964).
[1338] R. D. Rodman, ?A note on a set of test matrices for inversion,? Commun. ACM,6, No. 9, 515 (1963). · doi:10.1145/367593.367597
[1339] G. Rodrigue, ?A gradient method for the matrix eigenvalue problem Ax=?Bx,? Numer. Math.,22, No. 1, 1?16 (1973). · Zbl 0261.65031 · doi:10.1007/BF01436617
[1340] E. H. Rogers, ?A minimax theory for overdamped systems,? Arch. Ration. Mech. Anal.,16, 89?96 (1964). · Zbl 0124.07105 · doi:10.1007/BF00281333
[1341] T. R. Rogge and D. D. Walling, ?A note on the bordering method of inverting a matrix,? Am. Math. Mon.,73, No. 8, 879?880 (1966). · Zbl 0144.18103 · doi:10.2307/2314193
[1342] Ch. A. Rohde, ?Generalized inverses of partitioned matrices,? SIAM J. Appl. Math.,13, No. 4, 1033?1035 (1965). · Zbl 0145.03801 · doi:10.1137/0113070
[1343] Ch. A. Rohde, ?Some results on generalized inverses,? SIAM Rev.,8, No. 2, 201?205 (1966). · Zbl 0138.25303 · doi:10.1137/1008040
[1344] J. Rokne, ?Condition numbers of Pei matrices,? Commun. ACM,13, No. 12, 699 (1970). · Zbl 0212.16904 · doi:10.1145/362790.362812
[1345] J. Rokne, ?Fehlererfassung bei Eigenwertproblemen von Matrizen,? Computing,7, Nos. 3?4, 145?152 (1971). · Zbl 0221.65062 · doi:10.1007/BF02242342
[1346] J. Rokne, ?Automatic error bounds for simple zeros of analytic functions,? Commun. ACM,16, No. 2, 101?104 (1973). · Zbl 0248.65033 · doi:10.1145/361952.361962
[1347] J. Rokne and P. Lancaster, ?Complex interval arithmetic,? Commun. ACM,14, No. 2, 111?112 (1971). · Zbl 0213.16302 · doi:10.1145/362515.362563
[1348] W. Romberg and J. Aasen, ?Bestimmung einzehler Eigenwerte grosser symmetrischer Matrizen,? Wiss. Z. Hochsch. Archit. Bauwesen, Weimar,12, Nos. 5?6, 522?523 (1965). · Zbl 0163.38803
[1349] D. J. Rose, ?An algorithm for solving a special class of tridiagonal systems of linear equations,? Commun. ACM,12, No. 4, 234?236 (1969). · Zbl 0175.15805 · doi:10.1145/362912.362940
[1350] D. J. Rose and James R. Bunch, ?The role of partitioning in the numerical solution of sparse systems,? in: Sparse Matrices and Applications, Plenum Press, New York-London (1972), pp. 177?187.
[1351] D. J. Rose and R. A. Willoughby (eds.), Sparse Matrices and Their Applications, Plenum Press, New York-London (1972).
[1352] J. B. Rosen, ?Minimum and basic solutions to singular linear systems,? SIAM J. Appl. Math.,12, No. 1, 156?162 (1964). · Zbl 0156.16205 · doi:10.1137/0112014
[1353] J. B. Rosen, ?Chebyshev solution of large linear systems,? J. Comput. Syst. Sci.,1, 29?34 (1967). · Zbl 0148.39102 · doi:10.1016/S0022-0000(67)80005-9
[1354] R. Rosen, ?Matrix bandwidth minimization,? Proc. 23rd ACM Nat. Conf., Princeton, New Jersey-London (1968), pp. 585?595.
[1355] J. P. Roth, ?An application of algebraic topology; Kron’s method of tearing,? Q. Appl. Math.,17, 1?24 (1959). · doi:10.1090/qam/104337
[1356] A. Ruhe, ?On the quadratic convergence of the Jacobi method for normal matrices,? BIT,7, No. 4, 305?313 (1967). · Zbl 0159.20503 · doi:10.1007/BF01939324
[1357] A. Ruhe, ?On the quadratic convergence of a generalization of the Jacobi method to arbitrary matrices,? BIT,8, No. 3, 210?231 (1968). · Zbl 0177.43002 · doi:10.1007/BF01933422
[1358] A. Ruhe, ?Properties of a matrix with a very ill-conditioned eigenproblem,? Numer. Math.,15, No. 1, 57?60 (1970). · Zbl 0184.37704 · doi:10.1007/BF02165660
[1359] A. Ruhe, ?An algorithm for numerical determination of the structure of a general matrix,? BIT,10, No. 2, 196?216 (1970). · Zbl 0255.65023 · doi:10.1007/BF01936867
[1360] A. Ruhe, ?Perturbation bounds for means of eigenvalues and invariant subspaces,? BIT,10, No. 3, 343?354 (1970). · Zbl 0208.18302 · doi:10.1007/BF01934203
[1361] A. Ruhe, ?On the closeness of eigenvalue and singular values for almost normal matrices,? Rep. UMINF-41.73 (1973).
[1362] A. Ruhe, ?Iterative eigenvalue algorithms based on convergent splittings,? Rep. UMINF-43.73 (1973).
[1363] A. Ruhe, ?Algorithms for the nonlinear eigenvalue problem,? SIAM J. Numer. Anal.,10, No. 4, 674?689 (1973). · Zbl 0261.65032 · doi:10.1137/0710059
[1364] A. Ruhe, ?SOR-methods for the eigenvalue problem with large sparse matrices,? Math. Comput.,28, No. 127, 695?710 (1974). · Zbl 0304.65027
[1365] A. Ruhe, ?Iterative eigenvalue algorithms for large symmetric matrices,? Internat. Schrift. Numer. Math.,24, 97?115 (1974). · Zbl 0296.65016
[1366] A. Ruhe and T. Wiberg, ?The method of conjugate gradients used in inverse iteration,? BIT,12, No. 4, 543?554 (1972). · Zbl 0266.65033 · doi:10.1007/BF01932964
[1367] B. Rust, W. R. Burrus, and C. Schneeberger, ?A simple algorithm for computing the generalized inverse of a matrix,? Commun. ACM,9, No. 5, 381?385 (1966). · Zbl 0135.37401 · doi:10.1145/355592.365659
[1368] H. Rutishauser, ?Deflation by elementary rotation for the solution of algebraic eigenvalue problems,? Reprints of the 14th National Meeting of the Assoc. Comput. Mach., Cambridge, Mass. (1959).
[1369] H. Rutishauser, ?On a modification of the QD-algorithm with Graeffe-type convergence,? Proc. IFIP Congr. 62, Munich, 1962, North-Holland, Amsterdam (1963), pp. 93?96. · Zbl 0113.10702
[1370] H. Rutishauser, ?Stabile Sonderfalle des Quotienten-Differenzen-Algorithmus,? Numer. Math.,5, No. 2, 95?112 (1963). · Zbl 0196.48404 · doi:10.1007/BF01385882
[1371] H. Rutishauser, ?The LLT and QR methods for symmetric tridiagonal matrices,? Comput. J.,6, No. 2, 133 (1963). · Zbl 0117.10904 · doi:10.1093/comjnl/6.2.133
[1372] H. Rutishauser, ?Numerical experiments with the QD-transformation of J. G. F. Francis,? Proc. IFIP Congr. 62, Munich, 1972, North-Holland, Amsterdam (1963), pp. 198?200.
[1373] H. Rutishauser, ?On Jacobi rotation patterns,? Proc. Symp. Appl. Math.,15, 219?240, Am. Math. Soc., Providence, Rhode Island (1963). · Zbl 0135.37301
[1374] H. Rutishauser, ?Une methode pour le calcul des valeurs propres des matrices non symétriques,? C.R. Acad. Sci.,259, No. 17, A2758 (1964). · Zbl 0152.14704
[1375] H. Rutishauser, ?Bestimmung der Eigenwerte orthogonaler Matrizen,? Numer. Math.,9, No. 2, 104?108 (1966). · Zbl 0171.13406 · doi:10.1007/BF02166029
[1376] H. Rutishauser, ?The Jacobi method for real symmetric matrices,? Numer. Math.,9, No. 1, 1?10 (1966). · Zbl 0154.17002 · doi:10.1007/BF02165223
[1377] H. Rutishauser, ?On test matrices,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 349?365 (1968). · Zbl 0209.17502
[1378] H. Rutishauser, ?Once again: the least square problem,? Linear Algebra Appl.,1, No. 4, 479?488 (1968). · Zbl 0169.19502 · doi:10.1016/0024-3795(68)90022-0
[1379] H. Rutishauser, ?Computational aspects of F. L. Bauer’s simultaneous iteration method,? Numer. Math.,13, No. 1, 4?13 (1969). · Zbl 0182.21304 · doi:10.1007/BF02165269
[1380] H. Rutishauser, ?Simultaneous iteration method for symmetric matrices,? Numer. Math.,16, No. 3, 205?223 (1970). · Zbl 0239.65037 · doi:10.1007/BF02219773
[1381] H. Rutishauser and H. R. Schwarz, ?The LR transformation method for symmetric matrices,? Numer. Math.,5, No. 3, 273?289 (1963). · Zbl 0112.34801 · doi:10.1007/BF01385897
[1382] V. Saad, ?Etudes des translations d’origine dans les algorithmes LR et QR,? C. R. Acad. Sci.,A278, No. 2, 93?96 (1974). · Zbl 0277.65016
[1383] R. A. Sack, ?A fully stable rational version of the QR algorithm for tridiagonal matrices,? Numer. Math.,18, No. 5, 432?441 (1972). · Zbl 0221.65064 · doi:10.1007/BF01406680
[1384] M. K. Sain, ?On the control applications of a determinant equality related to eigenvalue computation,? IEEE Trans. Autom. Contr.,11, No. 1, 109?111 (1966). · doi:10.1109/TAC.1966.1098227
[1385] A. H. Sameh, ?On Jacobi and Jacobilike algorithms for a parallel computer,? Math. Comput.,25, No. 115, 579?590 (1971). · Zbl 0222.65046 · doi:10.1090/S0025-5718-1971-0297131-6
[1386] S. Sarman, ?Bemerkungen zu inversen Eigenwertproblemen,? Computing,4, No. 3, 207?215 (1969). · Zbl 0209.46703 · doi:10.1007/BF02234769
[1387] S. Sarman and J. Albrecht, ?Bemerkungen zur Iteration mit monoton zerlegbaren Operatoren,? Z. Angew. Math. Mech.,52, No. 11, 554?556 (1972). · Zbl 0249.65037 · doi:10.1002/zamm.19720520914
[1388] Tatuya Sasakawa, ?New method for solving eigenvalue problems,? J. Math. Phys.,4, No. 7, 970?992 (1963). · Zbl 0149.46103 · doi:10.1063/1.1704023
[1389] W. Sautter, ?Fehlerfortpflanzung und Rundsungsfohler bei der verallgemeinerten inversion von Matrizen,? Diss. Doct. Naturwiss. Fak. Allg. Wiss. Tech. Univ. München (1971).
[1390] I. R. Savage and E. Lukacs, ?Tables of inverses of finite segments of the Hilbert matrix,? Nat. Bur. Stand. Appl. Math. Ser.,39, 105?108 (1954). · Zbl 0058.01002
[1391] M. D. Sawhney, ?The computation of eigenvalues. I. Real symmetric matrices,? SIAM J. Appl. Math.,12, No. 4, 726?733 (1964). · Zbl 0131.14203 · doi:10.1137/0112060
[1392] Jürgen Schade, ?Kombination von Eizelschritt- und Relaxationsverfahren,? Diss. Dokt. Naturwiss. Abt. Math. Ruhr., Univ. Bochum (1973).
[1393] G. Schauer, ?Utilisation de quelques types de normes de vecteurs dans des méthodes iteratives de resolution de systemes linéaires,? These Doct. 3-e Cycl. Math. Appl. Fac. Sci., Univ. Grenoble (1962).
[1394] E. Schmid, ?An iterative procedure to compute the model matrix of eigenvectors,? J. Geophys. Res.,76, No. 8, 1916?1920 (1971). · Zbl 0214.41004 · doi:10.1029/JB076i008p01916
[1395] J. W. Schmidt, ?Ausgangsvektoren für monotone Iterationen bei linearen Gleichungssystemen,? Numer. Math.,6, No. 2, 78?88 (1964). · Zbl 0123.11102 · doi:10.1007/BF01386057
[1396] J. W. Schmidt, ?Konvergenzbeschleunigung bei monotonen Vektorfolgen,? Acta. Math. Acad. Sci. Hung.,16, Nos. 1?2, 221?229 (1965). · Zbl 0131.13901 · doi:10.1007/BF01886402
[1397] J. W. Schmidt, ?Fehlerabschatzung und Konvergenzbeschleunigung zu Iterationen bei linearen Gleichungssystemen,? Apl. Mat.,10, No. 3, 297?301 (1965).
[1398] J. W. Schmidt, ?Asymptotische Einschliessung bei konvergenzbeschleunigenden Verfahren,? Numer. Math.,8, No. 2, 105?113 (1966). · Zbl 0135.37903 · doi:10.1007/BF02163180
[1399] J. W. Schmidt, ?Asymptotische Einschliessung bei konvergenzbeschleunigenden Verfahren. II,? Numer. Math.,11, No. 1, 53?56 (1968). · Zbl 0155.19703 · doi:10.1007/BF02165471
[1400] A. J. Schneider, ?Generation of test matrices having certain sign patterns and prescribed positive spectra,? Commun. ACM,12, No. 7, 378?379 (1969). · Zbl 0182.48902 · doi:10.1145/363156.363161
[1401] A. J. Schneider, ?Estimate of the number of arithmetic operations required in the LU decomposition of a sparse matrix,? IEEE Trans. Circuit Theory,17, No. 2, 269?270 (1970). · doi:10.1109/TCT.1970.1083083
[1402] M. Schneider, ?Einschliessen der Lösung einer Gleichung durch ein Iterationsverfahren bei Iterationsverfahren bei iteration mit einem Näherungsoperator,? Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt,10, No. 5, 557?560 (1968). · Zbl 0276.65031
[1403] M. Schneider, ?Bemerkungen zur Erzwingung von Einschliessungsaussagen bei einem Iterationsverfahren,? Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt,10, No. 5, 561?564 (1968). · Zbl 0276.65032
[1404] A. Schönhage, ?Zur quadratischen Konvergenz des Jacobi-Verfahrens,? Numer. Math.,6, No. 5, 410?412 (1964). · Zbl 0221.65066 · doi:10.1007/BF01386091
[1405] A. Schönhage, ?Unitäre Transformationen grosser Matrizen,? Numer. Math.,20, No. 5, 409?417 (1973). · Zbl 0252.65031 · doi:10.1007/BF01402563
[1406] G. Schröder, ?Über die Konvergenz einiger Jacobi-Verfahren zur Bestimmung der Eigenwerte symmetrischer Matrizen,? Forschungsber. Landes Nordrhein-Westfalen, No. 2191, 59 (1964).
[1407] J. Schröder, ?Fehlerabschätzung bei linearen Gleichungssystemen mit dem brouwerschen Fixpunktsatz,? Arch. Ration. Mech. and Anal.,3, No. 1, 28?44 (1959). · Zbl 0099.11002 · doi:10.1007/BF00284162
[1408] J. Schröder, ?Lineare Operatoren mit positiver inversen,? Arch. Ration. Mech. Anal.,8, No. 5, 408?434 (1961). · Zbl 0104.08802 · doi:10.1007/BF00277453
[1409] J. Schröder, ?Computing error bounds in solving linear systems,? Math. Comput.,16, No. 79, 323?337 (1962). · Zbl 0105.10202 · doi:10.2307/2004052
[1410] G. Schulz, ?Iterative Berechnung der reziproken Matrix,? Z. Angew. Math. Mech.,13, No. 1, 57?59 (1933). · JFM 59.0535.04 · doi:10.1002/zamm.19330130111
[1411] H. R. Schwarz, ?Die Reduktion einer symmetrischen Bandmatrix auf tridiagonale Form,? Z. Angew. Math. Mech.,45, Sonderh., T75-T77 (1965). · Zbl 0223.65010
[1412] H. R. Schwarz, ?Tridiagonalization of a symmetric band matrix,? Numer. Math.,12, No. 4, 231?241 (1968). · Zbl 0165.50201 · doi:10.1007/BF02162505
[1413] H. R. Schwarz, Numerik Symmetrischer Matrizen, B. G. Teubner, Stuttgart (1968).
[1414] H. R. Schwarz, ?Die Methode der konjugierten Gradienten in der Ausgleichsrechnung,? Z. Vermessungswesen,95, 130?140 (1970). · Zbl 0215.55405
[1415] H. R. Schwarz, ?The eigenvalue problem (A ? ?B)x=0 for symmetric matrices of high order,? Comput. Methods Appl. Mech. Eng.,3, 11?28 (1974). · Zbl 0271.65027 · doi:10.1016/0045-7825(74)90039-5
[1416] H. R. Schwarz, ?The method of coordinate overrelaxation for (A ? ?B)x=0,? Numer. Math.,23, No. 2, 135?151 (1974). · Zbl 0278.65038 · doi:10.1007/BF01459947
[1417] H. R. Schwarz, H. Rutishauser, and E. Stiefel, Numerik Symmetrischer Matrizen, Teubner, Stuttgart (1972).
[1418] H. Schwerdtfeger, ?Remarks on the generalized inverse of a matrix,? Linear Algebra Appl.,1, No. 3, 325?328 (1968). · Zbl 0159.32002 · doi:10.1016/0024-3795(68)90012-8
[1419] J. E. Scroggs and P. L. Odell, ?An alternate definition of a pseudoinverse of a matrix,? SIAM J. Appl. Math.,14, No. 4, 796?810 (1966). · Zbl 0196.30103 · doi:10.1137/0114067
[1420] H. J. Scudder, ?Quick and dirty method of approximating the minimum or maximum eigenvalue and eigenvector of arbitrary matrix,? Proc. IEEE,53, No. 4, 415 (1965). · doi:10.1109/PROC.1965.3786
[1421] M. J. Seaton, ?Diagonalization of complex symmetric matrices using a modified Jacobi method,? Comput. J.,12, No. 2, 156?157 (1969). · Zbl 0176.13403 · doi:10.1093/comjnl/12.2.156
[1422] J. Segethova, ?Elimination on sparse symmetric systems of a special structure,? Apl. Mat.,17, No. 6, 448?460 (1972). · Zbl 0259.65035
[1423] J. Segethova, ?Gaussova eliminace pro systemy linearnich algebraickych rovnic a ridkymi maticemi,? Acta. Polytechnica, Prace ?VUT v Praze IY, Vedecka Konference, 59?64 (1973).
[1424] J. Seitz, ?A note to Cornock’s method for inversion of matrices,? Apl. Mat.,9, No. 6, 410?411 (1964). · Zbl 0134.13204
[1425] J. Seitz, ?A note on the approximation of one matrix by a matrix of another rank,? Cas. Pestov. Math.,91, No. 2, 121?124 (1966). · Zbl 0136.24902
[1426] Syamal Kumar Sen, ?On numerical measures of singularity of a matrix,? J. Indian Inst. Sci.,49, No. 2, 37?47 (1967).
[1427] Syamal Kumar Sen, ?On the derivation of the computational formulae of the orthogonalization method of inversion including experiments on near-singular matrices and on the transformation of 2-D array to 1-D array,? J. Indian Inst. Sci.,50, No. 1, 37?44 (1968).
[1428] Syamal Kumar Sen, ?On an automatic computation of characteristic roots of a matrix,? J. Indian Inst. Sci.,50, No. 3, 210?219a (1968).
[1429] Syamal Kumar Sen, ?On triangular decomposition to evaluate the determinant of an arbitrary square matrix A including the solution of Ax=b and on the related computational recurrence relations,? J. Indian Inst. Sci.,51, No. 3, 269?279 (1969).
[1430] Syamal Kumar Sen, ?The RL algorithm for finding eigenvalues of a matrix,? J. Indian Inst. Sci.,52, Nos. 2?3, 105?111 (1970).
[1431] Syamal Kumar Sen, ?Computation of matrix inverse by a power series method,? J. Indian Inst. Sci.,53, No. 1, 43?50 (1971).
[1432] Syamal Kumar Sen and E. V. Krishnamurthy, ?Rank-augmented LU-algorithm for computing generalized matrix inverses,? IEEE Trans. Comput.,23, No. 2, 199?201 (1974). · Zbl 0281.65026
[1433] Syamal Kumar Sen and P. V. Sankar, ?Triangular partitioning for matrix inversion,? Int. J. Control,15, No. 3, 571?575 (1972). · Zbl 0266.15001 · doi:10.1080/00207177208932173
[1434] A. Serge, ?Etude de méthodes numériques directes pour la résolution de systèmes d’équations linéaires sur I. B. M. 650 standard,? These Ingr. Doct. Fac. Sci. Univ. Nantes (1963).
[1435] J. S. Seward, ?Error correction in solutions of linear systems,? Industr. Math.,9, No. 1, 41?50 (1958).
[1436] L. F. Shampine, ?The condition of certain matrices,? J. Res. Nat. Bur. Stand.,B69, No. 4, 333?334 (1965). · Zbl 0178.51401 · doi:10.6028/jres.069B.034
[1437] G. Shapiro, ?Gauss elimination for singular matrices,? Math. Comput.,17, No. 84, 441?445 (1963). · Zbl 0114.32301 · doi:10.1090/S0025-5718-1963-0156451-1
[1438] I. Shavitt, ?Modification of Nesbert’s algorithm for the iterative evaluation of eigenvalues and eigenvectors of large matrices,? J. Comput. Phys.,6, No. 1, 124?130 (1970). · Zbl 0209.17701 · doi:10.1016/0021-9991(70)90010-0
[1439] I. Shavitt, C. F. Bender, A. Pipano, and R. P. Hosteny, ?The iterative calculation of several of the lowest or highest eigenvalues and corresponding eigenvectors of very large symmetric matrices,? J. Comput. Phys.,11, No. 1, 90?108 (1973). · Zbl 0253.65021 · doi:10.1016/0021-9991(73)90149-6
[1440] N. Shinozaki, M. Sibuya, and K. Tanabe, ?Numerical algorithms for the Moore -Penrose inverse of a matrix: iterative methods,? Ann. Inst. Statist. Math.,24, No. 3, 621?629 (1972). · Zbl 0314.65016 · doi:10.1007/BF02479787
[1441] I. Shirakawa and Ozaki H. Sakamoto, ?Sparsity-orientedordering of pivotal operations on network equations,? SIAM J. Appl. Math.,24, No. 1, 121?129 (1973). · Zbl 0233.94014 · doi:10.1137/0124012
[1442] Masaaki Sibuya, ?Subclassesof generalized inverses of matrices,? Ann. Inst. Statist. Math.,22, No. 3, 543?556 (1970). · Zbl 0233.15005 · doi:10.1007/BF02506375
[1443] I. H. Siegel, ?Deferment of computation in the method of least squares,? Math. Comput.,19, No. 90, 329?331 (1965). · Zbl 0143.17201 · doi:10.2307/2003361
[1444] M. Simaan, ?On the inverse of matrices with nearly equal elements,? Int. J. Numer. Meth. Eng.,5, No. 4, 589?591 (1973). · Zbl 0261.65023 · doi:10.1002/nme.1620050416
[1445] A. Simpson and B. Tabarrok, ?On Kron’s eigenvalue procedure and related methods of frequency analysis,? Q. J. Mech. Appl. Math.,21, No. 1, 1?39 (1968). · Zbl 0157.23504 · doi:10.1093/qjmam/21.1.1
[1446] M. Sisler, ?Prispever k iteracnim metodam reseni soustav linearnich rovnic s nesymetrickou matrici specialniho typu,? Cas. Pestov. Math.,90, No. 3, 337?343 (1965).
[1447] M. Sisler, ?Approximative Formeln für den Fehler bei Iterationsverfahren,? Appl. Mat.,11, No. 5, 341?351 (1966). · Zbl 0147.12703
[1448] M. Sisler, ?Über die Konvergenzbeschleunigung verschiedener Iterationsverfahren,? Appl. Mat.,12, No. 4, 255?267 (1967). · Zbl 0155.46802
[1449] M. Sisler, ?Über eine Relaxationsmethode,? Appl. Mat.,13, No. 6, 478?488 (1968). · Zbl 0184.37702
[1450] M. Sisler, ?Über die Konvergenzbeschleunigung komplexer Iterationsverfahren,? Appl. Mat.,15, No. 3, 156?176 (1970). · Zbl 0155.46802
[1451] M. Sisler, ?Über die Konvergenz von Iterations verfahren,? Appl. Mat.,16, No. 1, 10?23 (1971).
[1452] M. Sisler, ?Über ein Iterationsverfahren für zyklische Matrizen,? Appl. Mat.,17, No. 3, 225?233 (1972). · Zbl 0247.65020
[1453] M. Sisler, ?Über die Konvergenz eines gewissen Iterationsverfahrens für zyklische Matrizen,? Appl. Mat.,18, No. 2, 89?98 (1973). · Zbl 0258.65036
[1454] M. Sisler, ?Bemerkungen zur Optimierung eines gewissen Iterations Verfahrens,? Appl. Mat.,18, No. 5, 315?324 (1973). · Zbl 0267.65023
[1455] M. Sisler, ?Über ein zweiparametriges Iterationsverfahren,? Appl. Mat.,18, No. 5, 325?332 (1973). · Zbl 0267.65024
[1456] M. Sisler, ?Über die Konvergenz eines zweiparametrigen Iterations Verfahrens,? Appl. Mat.,18, No. 6, 452?461 (1973). · Zbl 0279.65030
[1457] W. Sitko, ?O pewnym sposobie przyspieszania zbieznosci ciagow iteracyjnych,? Zesz. Nauk. Politech. Slaskiej, No. 113, 55?62 (1964).
[1458] G. A. Sitton, ?A direct technique for improving a matrix inverse,? Comput. Project, Rice Univ., Houston, Texas, Rep. No. ORO 2572-10 (1966).
[1459] G. A. Sitton, ?Direct technique for improving a matrix inverse,? IBM J. Res. Develop.,15, No. 5, 413?417 (1971). · Zbl 0266.65027 · doi:10.1147/rd.155.0413
[1460] H. Skala, ?Einige Iterationsverfahren zur Inversion von Matrizen,? Elektron. Datenverarb.,7, No. 4, 191?193 (1965). · Zbl 0128.36404
[1461] A. van der Sluis, ?Equilibration and pivoting in linear algebraic systems,? in: Proc. IFIP Congr. 68, Edinburgh, 1968, Vol. I: Mathematics, Software, North-Holland, Amsterdam (1969), pp. 127?129.
[1462] S. van der Sluis, ?Condition numbers and equilibration of matrices,? Numer. Math.,14, No. 1, 14?23 (1969). · Zbl 0182.48906 · doi:10.1007/BF02165096
[1463] A. van der Sluis, ?Stability of solutions of linear algebraic systems,? Numer. Math.,14, No. 3, 246?251 (1970). · Zbl 0182.49001 · doi:10.1007/BF02163333
[1464] A. van der Sluis, ?Condition equilibration and pivoting in linear algebraic systems,? Numer. Math.,15, No. 1, 74?86 (1970). · Zbl 0182.49002 · doi:10.1007/BF02165662
[1465] A. van der Sluis, ?Stability of the solutions of linear least squares problems,? Gatlinburg VI Symposium on Numerical Algebra, München (1974). · Zbl 0308.65026
[1466] B. T. Smith, J. M. Boyle, B. S. Garbow, Y. Ikebe, V. C. Klema, and C. B. Moler, Maxtrix Eigensystem Routines -EISPACK Guide, Springer-Verlag, Berlin-Heidelberg-New York (1974). · Zbl 0289.65017
[1467] D. M. Smith and W. Orchard-Hays, ?Computational efficiency in product form LP codes,? in: Recent Advances Math. Programm., McGraw-Hill, New York-San Francisco-Toronto-London (1963), pp. 211?218.
[1468] R. A. Smith, ?The condition numbers of the matrix eigenvalue problem,? Numer. Math.,10, No. 3, 232?240 (1967). · Zbl 0189.47801 · doi:10.1007/BF02162166
[1469] W. W. Smith and S. Erdman, ?A note on the inversion of complex matrices,? IEEE Trans. Autom. Control,19, No. 1, 64 (1974). · Zbl 0276.15004 · doi:10.1109/TAC.1974.1100466
[1470] T. Söderstrom and G. W. Stewart, ?On the numerical properties of an iterative method for computing the Moore-Penrose generalized inverse,? SIAM J. Numer. Anal.,11, No. 1, 61?74 (1974). · Zbl 0241.65038 · doi:10.1137/0711008
[1471] W. R. Spillers, ?Analysis of large structures; Kron’s method and more recent work,? J. Struct. Div. ASCE 94 ST-11, 2521?2534 (1968).
[1472] W. R. Spillers and N. Hickerson, ?Optimal elimination for sparse symmetric systems as a graph problem,? Q. Appl. Math.,26, No. 3, 425?432 (1968). · Zbl 0164.20102 · doi:10.1090/qam/233497
[1473] V. P. Sreedharan, ?Solutions of overdetermined linear equations which minimize error in an abstract norm,? Numer. Math.,13, No. 2, 146?151 (1969). · Zbl 0185.40603 · doi:10.1007/BF02163232
[1474] V. P. Sreedharan, ?Least squares algorithm for finding solutions of overdetermined linear equations which minimize error in an abstract norm,? Numer. Math.,17, No. 5, 387?401 (1971). · Zbl 0231.65040 · doi:10.1007/BF01436088
[1475] W. T. Stallings and T. L. Boullion, ?Computation of pseudoinverse matrices using residue arithmetic,? SIAM Rev.,14, No. 1, 152?163 (1972). · Zbl 0238.65016 · doi:10.1137/1014005
[1476] W. T. Stallings and T. L. Boullion, ?The pseudoinverse of an r-circulant matrix,? Proc. Am. Math. Soc.,34, 385?388 (1972). · Zbl 0222.15002
[1477] D. V. Steward, ?On an approach to techniques for the analysis of the structure of large systems of equations,? SIAM Rev.,4, No. 4, 321?342 (1962). · Zbl 0112.34602 · doi:10.1137/1004088
[1478] D. V. Steward, ?Partitioning and tearing systems of equations,? SIAM J. Numer. Anal.,2, No. 2, 345?365 (1965). · Zbl 0141.13502
[1479] D. V. Steward, ?Tearing analysis of the structure of disorderly sparse matrices,? in: Sparse Matrix Proceedings, R. A. Willoughby (ed.), RA I No. 11707, IBM Corp. Thomas J. Watson Res. Center, Yorktown Heights, New York (1969), Chap. XXII, pp. 65?74.
[1480] G. W. Stewart, ?Accelerating the orthogonal iteration for the eigenvectors of a Hermitian matrix,? Numer. Math.,13, No. 4, 362?376 (1969). · Zbl 0185.40203 · doi:10.1007/BF02165413
[1481] G. W. Stewart, ?A set theoretic formulation of backward rounding error analysis,? Univ. Texas Comput. Center, JMN-92 (1969).
[1482] G. W. Stewart, ?Incorporating origin shifts into the QR algorithm for symmetric tridiagonal matrices,? Commun. ACM,13, No. 6, 365?367 (1970). · Zbl 0195.45001 · doi:10.1145/362384.362501
[1483] G. W. Stewart, ?On the sensitivity of the eigenvalue problem Ax=?Bx,? Center Numer. Anal. Univ. Texas, Austin, CNA-13 (1971).
[1484] G. W. Stewart, ?On the sensitivity of the eigenvalue problem Ax=?Bx,? SIAM J. Numer. Anal.,9, No. 4, 669?686 (1972). · Zbl 0252.65026 · doi:10.1137/0709056
[1485] G. W. Stewart, ?Error and perturbation bounds for subspaces associated with certain eigenvalue problems,? SIAM Rev.,15, No. 4, 727?764 (1973). · Zbl 0297.65030 · doi:10.1137/1015095
[1486] G. W. Stewart, ?Conjugate direction methods for solving systems of linear equations,? Numer. Math.,21, No. 4, 285?297 (1973). · Zbl 0253.65017 · doi:10.1007/BF01436383
[1487] G. W. Stewart, Introduction to Matrix Computations, Academic Press, New York (1973), Chap. XIII. · Zbl 0302.65021
[1488] G. W. Stewart, ?Perturbation bounds for the QR factorization of a matrix,? Univ. Maryland Computer Sci. Dept., Tech. Rep. 323 (1974).
[1489] G. W. Stewart, ?Modifying pivot elements in Gaussian elimination,? Math. Comput.,28, No. 126, 537?542 (1974). · Zbl 0293.65015 · doi:10.1090/S0025-5718-1974-0343559-8
[1490] G. W. Stewart, ?Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices,? Gatlinburg VI Symposium on Numerical Algebra, München (1974). · Zbl 0328.65025
[1491] E. L. Stiefel, ?Über diskrete und lineare Tschebyscheff-Approximationen,? Numer. Math.,1, No. 1, 1?28 (1959). · Zbl 0083.11501 · doi:10.1007/BF01386369
[1492] J. Stoer, ?A characterization of Holder norms,? SIAM J. Appl. Math.,12, No. 3, 634?648 (1964). · Zbl 0196.29803 · doi:10.1137/0112054
[1493] J. Stoer, ?On the characterization of least upper bounds norms in matrix space,? Numer. Math.,6, No. 4, 302?314 (1964). · Zbl 0126.32101 · doi:10.1007/BF01386078
[1494] J. Stoer, ?Lower bounds of matrices,? Numer. Math.,12, No. 2, 146?158 (1968). · Zbl 0174.31902 · doi:10.1007/BF02173409
[1495] J. Stoer and R. Bulirsch, Einführung in die Numerische Mathematik, Bd. 2 (Unter Berücksichtigung von Vorlesungen von F. L. Bauer), Springer-Verlag, Berlin (1973), Chap. IX. · Zbl 0257.65001
[1496] J. Stoer and C. Witzgall, ?Trans for mations by diagonal matrices in a normed space,? Numer. Math.,4, No. 2, 158?171 (1962). · Zbl 0117.11101 · doi:10.1007/BF01386309
[1497] M. Stojakovic, ?Determinanten rechteckiger Matrizen,? Vesn. Drushtva Mat. Fiz. Nar. Rep. Srbije,4, Nos. 1?2, 9?23 (1952).
[1498] M. Stojakovi?, ?Sur les matrices quasiinverses et les matrices quasiunites,? C. R. Acad. Sci.,236, No. 9, 877?879 (1953).
[1499] M. Stojakovic, ?Sur une proprieté des matrices quasi-inverses,? Vesn. Drushtva Mat. Fiz. Nar. Rep. Srbije,13, Nos. 3?4, 154?157 (1954).
[1500] H. S. Stone, ?An efficient parallel algorithm for the solution of a tridiagonal linear system of equations,? J. Assoc. Comput. Mach.,20, No. 1, 27?38 (1973). · Zbl 0269.65018 · doi:10.1145/321738.321741
[1501] V. Strassen, ?Gaussian elimination is not optimal,? Numer. Math.,13, No. 4, 354?356 (1969). · Zbl 0185.40101 · doi:10.1007/BF02165411
[1502] T. Ström, ?Minimization of norms and logarithmic norms by diagonal similarities,? Computing,10, Nos. 1?2, 1?7 (1972). · Zbl 0251.65034 · doi:10.1007/BF02242378
[1503] J. Svejda, ?Totalni chyba reseni linearnich algebraickych rovnic, ktere lze resit iteracemi,? Sb. Pr. VSD a VUD, No. 19, 53?64 (1969).
[1504] M. Svoboda and M. Sahm, ?Some comments on the equation block solver,? Int. J. Numer. Meth. Eng.,7, No. 2, 227?228 (1973). · doi:10.1002/nme.1620070212
[1505] System/360 Scientific Subroutine Package (360A-CM-03x), Version III, Programmers Manual, Fourth Edition, IBM Tech. Publ., New York.
[1506] F. Szidarovszky, ?Papers on matrix analysis,? Dept. Math. K. Marx Univ. Econ., Budapest (Publs.), No. 10 (1970).
[1507] F. Szidarovszky, ?Egy iteracios eljarasrol,? Magy. Tud. Akad. Mat. Fiz. Tud. Oszt. Közl.,20, Nos. 3?4, 395?397 (1971).
[1508] D. Szynal and J. Szynal, ?A propos de l’inversion des matrices généralisées de Jacobi,? Apl. Mat.,17, No. 1, 28?32 (1972). · Zbl 0246.15006
[1509] I. Takahashi, ?A note on the conjugate gradient method,? Inf. Process. Jpn.,5, 45?49 (1965). · Zbl 0147.13102
[1510] K. Tanabe, ?Projection method for solving a singular system of linear equations and its applications,? Numer. Math.,17, No. 3, 203?214 (1971). · Zbl 0228.65032 · doi:10.1007/BF01436376
[1511] K. Tanabe, ?An adaptive acceleration of general linear iterative processes for solving a system of linear equations,? Proc. 5th Haw. Int. Conf. Syst. Sci., Honolulu, Haw., 1972, Hollywood, Calif., 116?118 (1972).
[1512] K. Tanabe, ?Characterization of linear stationary iterative processes for solving a singular system of linear equations,? Numer. Math.,22, No. 5, 349?359 (1974). · Zbl 0312.65031 · doi:10.1007/BF01436918
[1513] I. C. Tang, ?A simple algorithm for solving linear equations of a certain type,? Z. Angew. Math. Mech.,49, No. 8, 508 (1969). · doi:10.1002/zamm.19690490808
[1514] J. C. Tardy, ?Etude des erreurs d’arrondi et de leur influence dans les calculatrices électroniques,? Constr. Metall.,3, No. 2, 12?17 (1966).
[1515] P. J. Taylor, ?A generalization of systematic relaxation methods for consistently ordered matrices,? Numer. Math.,13, No. 5, 377?395 (1969). · Zbl 0257.65038 · doi:10.1007/BF02163267
[1516] G. J. Tee, ?Eigenvectors of the successive overrelaxation process and its combination with Chebyshev semiiteration,? Comput. J.,6, No. 3, 250?263 (1963). · Zbl 0131.14106 · doi:10.1093/comjnl/6.3.250
[1517] R. P. Tewarson, ?On the product form of inverses of sparse matrices,? SIAM Rev.,8, No. 3, 336?342 (1966). · Zbl 0222.65050 · doi:10.1137/1008066
[1518] R. P. Tewarson, ?The product form of inverses of sparse matrices and graph theory,? SIAM Rev.,9, No. 1, 91?99 (1967). · Zbl 0168.13302 · doi:10.1137/1009004
[1519] R. P. Tewarson, ?A direct method for generalized matrix inversion,? SIAM J. Numer. Anal.,4, No. 4, 499?507 (1967). · Zbl 0153.46102 · doi:10.1137/0704045
[1520] R. P. Tewarson, ?Solution of a system of simultaneous linear equations with a sparse coefficient matrix by elimination methods,? BIT,7, No. 3, 226?239 (1967). · Zbl 0222.65051 · doi:10.1007/BF01939264
[1521] R. P. Tewarson, ?Row-column permutation of sparse matrices,? Comput. J.,10, No. 3, 300?305 (1967). · Zbl 0155.46902 · doi:10.1093/comjnl/10.3.300
[1522] R. P. Tewarson, ?A computational method for evaluating generalized inverses,? Comput. J.,10, No. 4, 411?413 (1968). · Zbl 0167.15602 · doi:10.1093/comjnl/10.4.411
[1523] R. P. Tewarson, ?Solution of linear equations with coefficient matrix in band form,? BIT,8, No. 1, 53?58 (1968). · Zbl 0157.22503 · doi:10.1007/BF01939979
[1524] R. P. Tewarson, ?On the orthonormalization of sparse vectors,? Computing,3, No. 4, 268?279 (1968). · Zbl 0174.46802 · doi:10.1007/BF02235393
[1525] R. P. Tewarson, ?On the Chebyshev solution of inconsistent linear equations,? BIT,8, No. 3, 232?242 (1968). · Zbl 0187.10302 · doi:10.1007/BF01933423
[1526] R. P. Tewarson, ?Projection methods for solving sparse linear systems,? Comput. J.,12, No. 1, 77?80 (1969). · Zbl 0164.46103 · doi:10.1093/comjnl/12.1.77
[1527] R. P. Tewarson, ?The Crout reduction for sparse matrices,? Comput. J.,12, No. 2, 158?159 (1969). · Zbl 0182.21301 · doi:10.1093/comjnl/12.2.158
[1528] R. P. Tewarson, ?On some representation of generalized inverses,? SIAM Rev.,11, No. 2, 272?276 (1969). · Zbl 0175.45804 · doi:10.1137/1011045
[1529] R. P. Tewarson, ?On computing generalized inverses,? Computing,4, No. 2, 139?152 (1969). · Zbl 0182.21203 · doi:10.1007/BF02234761
[1530] R. P. Tewarson, ?A least squares iterative method for singular equations,? Comput. J.,12, No. 4, 388?392 (1969). · Zbl 0185.40702 · doi:10.1093/comjnl/12.4.388
[1531] R. P. Tewarson, ?The Gaussian elimination and sparse systems,? in: Sparse Matrix Proceedings, R. A. Willoughby (ed.), RA I No. 11707, IBM Corp. Thomas J. Watson Res. Center, Yorktown Heights, New York (1969), Chap. XXII, pp. 35?42.
[1532] R. P. Tewarson, ?Computations with sparse matrices,? SIAM Rev.,12, No. 4, 527?543 (1970). · Zbl 0209.46602 · doi:10.1137/1012103
[1533] R. P. Tewarson, ?On the transformation of symmetric sparse matrices to the triple diagonal form,? Int. J. Comput. Math.,2, No. 3, 247?258 (1970). · Zbl 0233.65027 · doi:10.1080/00207167008803037
[1534] R. P. Tewarson, ?On the reduction of a sparse matrix to Hessenberg form,? Int. J. Comput. Math.,2, No. 4, 283?295 (1970). · Zbl 0231.65041 · doi:10.1080/00207167008803041
[1535] R. P. Tewarson, ?On two direct methods for computing generalized inverses,? Computing,7, Nos. 3?4, 236?239 (1971). · Zbl 0222.65049 · doi:10.1007/BF02242350
[1536] R. P. Tewarson, ?An iterative method for computing generalized inverses,? Int. J. Comput. Math.,3, No. 1, 65?74 (1971). · Zbl 0227.65028 · doi:10.1080/00207167108803052
[1537] R. P. Tewarson, ?Sorting and ordering sparse linear systems,? in: Large Sparse Sets of Linear Equations, Academic Press, London-New York (1971), pp. 151?167.
[1538] R. P. Tewarson, ?On the Gaussian elimination method for inverting sparse matrices,? Computing,9, No. 1, 1?7 (1972). · Zbl 0234.65038 · doi:10.1007/BF02236371
[1539] R. P. Tewarson, ?Solution of linear equations in remote sensing and picture reconstruction,? Computing,10, No. 3, 221?230 (1972). · Zbl 0251.65031 · doi:10.1007/BF02316909
[1540] R. P. Tewarson, ?On minimax solutions of linear equations,? Comput. J.,15, No. 3, 277?279 (1972). · Zbl 0259.65047 · doi:10.1093/comjnl/15.3.277
[1541] R. P. Tewarson, Sparse Matrices, Academic Press, New York-London (1973), Chap. XV. · Zbl 0262.65021
[1542] R. P. Tewarson and K. Y. Cheng, ?A desirable form for sparse matrices when computing their inverse in factored forms,? Computing,11, No. 1, 31?38 (1973). · Zbl 0258.65035 · doi:10.1007/BF02239469
[1543] R. P. Tewarson and P. Narain, ?Solution of linear equations resulting from satellite remote soundings,? J. Math. Anal. Appl.,47, No. 1, 1?14 (1974). · Zbl 0284.65024 · doi:10.1016/0022-247X(74)90032-8
[1544] R. P. Tewarson and P. Narain, ?Generalized inverses and resolution in the solution of linear equations,? Computing,13, No. 1, 81?88 (1974). · Zbl 0284.65034 · doi:10.1007/BF02268393
[1545] R. P. Tewarson and B. Ramnath, ?Some comments on the solution of linear equations,? BIT,9, No. 2, 167?173 (1969). · Zbl 0184.19605 · doi:10.1007/BF01933252
[1546] M. Tienari, ?A statistical model of roundoff error for varying length floating-point arithmetic,? BIT,10, No. 3, 355?365 (1970). · Zbl 0213.16203 · doi:10.1007/BF01934204
[1547] Th. C. T. Ting, ?A method of solving a system of linear equations whose coefficients form a tridiagonal matrix,? Q. Appl. Math.,22, No. 2, 105?116 (1964). · Zbl 0139.31802 · doi:10.1090/qam/168114
[1548] W. F. Tinney and W. S. Meyer, ?Solution of large sparse systems by ordered triangular factorization,? IEEE Trans. Autom. Control.,18, No. 4, 333?346 (1973). · Zbl 0272.90039 · doi:10.1109/TAC.1973.1100352
[1549] W. F. Tinney and E. C. Ogbuobiri, Sparsity Techniques: Theory and Practice, Rep. Bonville Power Administration, Portland, Oregon (1970).
[1550] W. F. Tinney and J. W. Walker, ?Direct solutions of sparse network equations by optimally ordered triangular factorization,? Proc. IEEE,55, No. 11, 1801?1809 (1967). · doi:10.1109/PROC.1967.6011
[1551] A. R. Tipton and H. W. Milnes, ?Least squares solution of linear equations,? Ind. Math.,22, Part 1, 11?16 (1972).
[1552] J. G. Todd, ?The problem of error in digital computation,? in: Error in Digital Computation, Vol. 1, Wiley, New York-London-Sydney (1965), pp. 3?41. · Zbl 0171.12802
[1553] J. A. Todd, ?Optimal ADI-parameters,? Int. Ser. Numer. Math. 7, Basel-Stuttgart S. Fr. 29, 58?70 (1967). · Zbl 0153.46503
[1554] J. A. Todd, ?Inequalities of Chebyshev, Zolotoreff, Cauer and W. B. Jordan,? Proc. Conf. at Dayton, Ohio, on Inequalities, Academic Press, New York (1967), pp. 321?328.
[1555] J. A. Todd, ?On condition numbers,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 141?159 (1968).
[1556] L. Todor, ?Distan?a euclidiana a unei matrici la mul?imea matricilor singulare,? Stud, ?i Cerc. Mat.,18, No. 2, 315?319 (1966).
[1557] L. Todor, ?Asupra metodei lui Jacobi de rezolvare a problemei vectorilor ?i valorilor proprii ale unei matrici simetrice,? Stud. Si Cerc. Mat.,18, No. 5, 637?640 (1966).
[1558] L. Todor, ?Problema normarii datelor pentru aplicarea metodei lui Jacobi respectiv Givens de rezolvare a problemei valorilor ?i vectorilor proprii pentru matrici simetrice,? Stud, si Cerc. Mat.,19, No. 1, 41?46 (1967).
[1559] L. Todor, ?Matricea ortogonalä cea mai apropiata de o matrice reala data,? Stud, si Cerc. Mat.,19, No. 3, 363?370 (1967).
[1560] S. Toman and J. Pliva, ?The multiplicity of solutions of the inverse secular problem,? J. Mol. Spectry,21, 362?371 (1966). · doi:10.1016/0022-2852(66)90162-7
[1561] Tatsuo Torii, ?Inversion of tridiagonal matrices and the stability of tridiagonal systems of linear equations,? Tech. Rep. Osaka Univ.,16, Nos. 716?747, 403?414 (1966).
[1562] Jjubomir B. Tosovic, ?Some experiments on sparse sets of linear equations,? SIAM J. Appl. Math.,25, No. 2, 142?148 (1973). · Zbl 0239.65034 · doi:10.1137/0125018
[1563] Clos J. du Tournyol, ?Note sur la decomposition matricielle triangulaires. Application à l’inversion matricielle et la résolution des systèmes linéaires,? Rev. Franc. Inform. et Rech. Oper.,1, No. 3, 83?91 (1967). · Zbl 0155.46803
[1564] Robinson Treitel, ?High-resolution digital filters,? Trans. Geosci. Electron., 36?38 (1966).
[1565] W. F. Trench, ?An algorithm for the inversion of finite Toeplitz matrices,? SIAM J. Appl. Math.,12, No. 3, 515?522 (1964). · Zbl 0131.36002 · doi:10.1137/0112045
[1566] W. F. Trench, ?An algorithm for the inversion of finite Hankel matrices,? SIAM J. Appl. Math.,13, No. 4, 1102?1107 (1965). · Zbl 0135.17801 · doi:10.1137/0113078
[1567] W. F. Trench and P. A. Scheinok, ?On the inversion of a Hilbert type matrix,? SIAM Rev.,8, No. 1, 57?61 (1966). · Zbl 0136.11802 · doi:10.1137/1008004
[1568] Nai-Kuan Tsao and F. F. Kuo, ?On machine precision, computation error and condition number in solving linear algebraic systems,? Comput. Elec. Eng.,1, No. 3, 459?464 (1973). · Zbl 0334.65025 · doi:10.1016/0045-7906(73)90010-4
[1569] R. R. Tucker, ?The ?2-process and related topics,? Pac. J. Math.,22, No. 2, 349?359 (1967). · Zbl 0166.06702 · doi:10.2140/pjm.1967.22.349
[1570] R. R. Tucker, ?The ?2-process and related topics. II,? Pac. J. Math.,28, No. 2, 455?463 (1969). · Zbl 0169.07002 · doi:10.2140/pjm.1969.28.455
[1571] A. D. Tuff and A. Jennings, ?An iterative method for large systems of linear structural equations,? Int. J. Numer. Meth. Eng.,7, No. 2, 175?183 (1973). · Zbl 0259.73040 · doi:10.1002/nme.1620070207
[1572] P. J. Turinsky, ?The supervariational technique revisited,? J. Math. Anal. Appl.,33, No. 3, 605?615 (1971). · Zbl 0219.65038 · doi:10.1016/0022-247X(71)90080-1
[1573] Katsuji Uosaki and Hiroshi Sugiyama, ?Explosive method for matrix inversion,? Tech. Rep. Osaka Univ.,20, 1?8 (1970).
[1574] N. S. Urquhart, ?Computation of generalized inverse matrices which satisfy specified conditions,? SIAM Rev.,10, No. 2, 216?218 (1968). · Zbl 0157.07003 · doi:10.1137/1010035
[1575] N. S. Urquhart, ?The nature of the lack of uniqueness of generalized inverse matrices,? SIAM Rev.,11, No. 2, 268?271 (1969). · Zbl 0177.04903 · doi:10.1137/1011044
[1576] J. S. Vandergraft, ?Generalized Rayleigh methods with applications to finding eigenvalues of large matrices,? Linear Algebra Appl.,4, No. 4, 353?368 (1971). · Zbl 0222.65047 · doi:10.1016/0024-3795(71)90006-1
[1577] J. S. Vandergraft, ?Applications of partial orderings to the study of positive definiteness, monotonicity, and convergence of iterative methods for linear systems,? SIAM J. Numer. Anal.,9, No. 1, 97?104 (1972). · Zbl 0204.48201 · doi:10.1137/0709011
[1578] J. Vanicek, ?Solution of special types of extended systems of linear equations with fully regular matrix on the computer,? Inf. Process. Machines, No. 15, 19?33 (1971).
[1579] J. M. Varah, ?The computation of bounds for the invariant subspace of a general matrix operator,? Computer Sci. Dept., Stanford Univ., Tech. Rep. CS 66 (1967).
[1580] J. M. Varah, ?The calculation of the eigenvectors of a general complex matrix by inverse iteration,? Math. Comput.,22, No. 104, 785?791 (1968). · Zbl 0174.46903 · doi:10.1090/S0025-5718-68-99868-2
[1581] J. M. Varah, ?Rigorous machine bounds for the eigensystem of a general complex matrix,? Math. Comput.,22, No. 104, 793?801 (1968). · Zbl 0176.13503 · doi:10.1090/S0025-5718-68-99867-0
[1582] J. M. Varah, ?Computing invariant subspaces of a general matrix when the eigensystem is poorly conditioned,? Math. Comput.,24, No. 109, 137?149 (1970). · Zbl 0195.45101 · doi:10.1090/S0025-5718-1970-0264843-9
[1583] J. M. Varah, ?Invariant subspace perturbations for a nonnormal matrix,? Proc. IFIP Congr. 71, Ljubljana, 1971, Vol. 2, North-Holland, Amsterdam-London (1972), pp. 1251?1253.
[1584] J. M. Varah, ?On the solution of block-tridiagonal systems arising from certain finite-difference equations,? Math. Comput.,26, No. 120, 859?868 (1972). · Zbl 0266.65029 · doi:10.1090/S0025-5718-1972-0323087-4
[1585] J. M. Varah, ?On the numerical solution of ill-conditioned linear systems with applications to ill-posed problems,? SIAM J. Numer. Anal.,10, No. 2, 257?267 (1973). · Zbl 0261.65034 · doi:10.1137/0710025
[1586] D. E. Varberg, ?The characteristic polynomial of a singular matrix,? Am. Math. Mon.,75, No. 5, 506 (1968). · Zbl 0162.33502 · doi:10.2307/2314710
[1587] G. Varga, ?Matrixok sajatekeinek meghatarozasa a ?hasonlosagi eliminacio? modszerevel,? Közl. Magyar Tud. Akad. Szamitastech. Közp.,5, 28?32 (1969).
[1588] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey (1962),. Chap. XIV. · Zbl 0133.08602
[1589] R. S. Varga, ?On variants of successive overrelaxation and alternating direction. Implicit methods,? Proc. IFIP Congr. 62, Munich, 1962, North-Holland, Amsterdam (1963), pp. 203?204.
[1590] R. S. Varga, ?Iterative methods for solving matrix equations,? Am. Math. Mon.,72, No. 2, Part 2, 67?74 (1965). · Zbl 0151.21402 · doi:10.2307/2313312
[1591] J. H. Verner and M. J. M. Bernai, ?On generalizations of the theory of consistent orderings for successive overrelaxation methods,? Numer. Math.,12, No. 3, 215?222 (1968). · Zbl 0172.18802 · doi:10.1007/BF02162914
[1592] J. Vignes and M. La Porte, ?Error analysis in computing,? Paris Univ., Inst. de Programmation (1973). · Zbl 0295.65035
[1593] J. A. Ville, ?De l’inversion des matrices,? Pubis. Inst. Statist. Univ. Paris,11, No. 3, 267?272 (1962).
[1594] P. V. Villumsen, ?On the solution of normal equations,? BIT,5, No. 3, 203?210 (1965). · Zbl 0128.36403 · doi:10.1007/BF01940222
[1595] R. de Vogelaere, ?Overrelaxations,? Abstract No. 539?553, Notices Am. th. Soc.,5, 147 (1958).
[1596] R. P. Voith, W. G. Vogt, and M. H. Mickle, ?On the computation of the generalized inverse by classical minimization,? Computing,9, No. 3, 175?187 (1972). · Zbl 0254.65029 · doi:10.1007/BF02246728
[1597] Prignano Ernesto de Volpe, ?Considerazioni sopra un procedimento per la stima degli autovalori di una matrice simmetrica,? Rend. Mat. Appl.,22, Nos 3?4, 439?446 (1963) (1964).
[1598] H. J. de Vries, ?On the eigenproblem for normal matrices,? Numer. Math.,21, No. 1, 37?42 (1973). · Zbl 0247.65023 · doi:10.1007/BF01436185
[1599] E. L. Wachspress, ?A generalized two-space dimension multigroup coding for the IBM-714,? Rep. KAPL-1724, Knolls Atomic Power Lab., Schenectady, New York (1957).
[1600] E. L. Wachspress, ?Extended application of alternating direction implicit iteration model problem theory,? SIAM J. Appl. Math.,11, No. 4, 994?1016 (1963). · Zbl 0244.65045 · doi:10.1137/0111073
[1601] E. L. Wachspress, ?Recent ADI theory and results for elliptic equations. Linear algebraic systems,? Proc. IFIP Congr. 65, New York City, 1965, Vol. 2, Spartan Books, Washington, MacMillan, London (1966).
[1602] E. L. Wachspress, Iterative Solution of Elliptic Systems and Application to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, Englewood Cliffs, New Jersey (1966), Chap. XIV. · Zbl 0161.12203
[1603] E. L. Wachspress, ?Solution of the ADI minimax problem,? Knolls Atomic Power Laboratory, Kapl-3448 (1968).
[1604] E. L. Wachspress, ?Iteration parameters in the numerical solution of elliptic problems,? Lect. Notes Math.,193, 93?109 (1971). · doi:10.1007/BFb0060344
[1605] T. Wakasugi and K. Kawamo, ?An efficient solution of a sparse set of simultaneous algebraic equations in structural analysis,? Proc. 20th Jpn. Nat. Congr. Appl. Mech., 1970, Tokyo, 145?152 (1971).
[1606] Y. Wallach and A. Barlevi, ?Algorithm 15. Inversion of a blockwise tridiagonal matrix,? Computing,7, Nos. 3?4, 357?363 (1971). · Zbl 0221.68026 · doi:10.1007/BF02242362
[1607] A. Wallis, D. L. S. McElwain, and H. O. Pritchard, ?The variation method and the algebraic eigenvalue problem,? Int. J. Quant. Chem.,3, No. 5, 711?722 (1969). · doi:10.1002/qua.560030515
[1608] J. Walsh, ?Direct and indirect methods,? in: Large Sparse Sets of Linear Equations, Academic Press, London-New York (1971), pp. 41?55.
[1609] W. L. Waltmann and R. J. Lambert, ?T-algorithm for tridiagonalization,? SIAM J. Appl. Math.,13, No. 4, 1069?1078 (1965). · Zbl 0219.65040 · doi:10.1137/0113074
[1610] H. H. Wang and R. T. Gregory, ?On the reduction of an arbitrary real square matrix to tridiagonal form,? Math. Comput.,18, No. 87, 501?505 (1964). · Zbl 0262.65030 · doi:10.1090/S0025-5718-1964-0165670-0
[1611] Jin-Ru Wang and Chin-Ju Wang, ?A gradient method for finding the eigenvalues and eigenvectors of a self-adjoint operator,? Chinese Math.,4, 24?30 (1963).
[1612] Jin-Ru Wang and Chin-Ju Wang, ?Gradient methods for finding eigenvalues and eigenvectors,? Chinese Math.,5, 578?587 (1964).
[1613] J. F. Ward, T. L. Boullion, and T. O. Lewis, ?A note on the oblique matrix pseudoinverse,? SIAM J. Appl. Math.,20, No. 2, 173?175 (1971). · Zbl 0218.15005 · doi:10.1137/0120022
[1614] J. F. Ward, T. L. Boullion, and T. O. Lewis, ?Weighted pseudoinverses with singular weights,? SIAM J. Appl. Math.,21, No. 3, 480?482 (1971). · Zbl 0236.15008 · doi:10.1137/0121051
[1615] J. F. Ward, T. L. Boullion, and T. O. Lewis, ?Weak spectral inverses,? SIAM J. Appl. Math.,22, No. 3, 514?518 (1972). · Zbl 0246.15005 · doi:10.1137/0122045
[1616] G. A. Watson, ?An algorithm for the inversion of block matrices of Toeplitz form,? J. Assoc. Comput. Mach.,20, No. 3, 409?415 (1973). · Zbl 0271.65020 · doi:10.1145/321765.321773
[1617] Per-Ake Wedin, ?Perturbation bounds in connection with singular value decomposition,? BIT,12, No. 1, 99?111 (1972). · Zbl 0239.15015 · doi:10.1007/BF01932678
[1618] Per-Ake Wedin, ?Perturbation theory for pseudoinverses,? BIT,13, No. 2, 217?232 (1973). · Zbl 0263.65047 · doi:10.1007/BF01933494
[1619] D. P. Wei, ?A multiple-precision modification of the Danilevsky method,? Computing Lab., Brown Univ. (1963).
[1620] H. F. Weinberger, ?A posteriori error bounds in iterative matrix inversion,? in: Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965), Academic Press, New York (1966), pp. 153?163.
[1621] H. Werner, Praktische Mathematik. I. Methoden der Linearen Algebra (Math. Scr., I), Springer-Verlag, Berlin (1970), Chap. X.
[1622] J. R. Westlake, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations, Wiley, New York (1968), Chap. VIE. · Zbl 0155.19901
[1623] P. A. White and R. R. Brown, ?A comparison of methods for computing the eigenvalues and eigenvectors of a real symmetric matrix,? Math. Comput.,18, No. 87, 457?463 (1964). · Zbl 0119.33202
[1624] T. M. Whitney and R. K. Meany, ?Two algorithms related to the method of steepest descent,? SIAM J. Numer. Anal.,4, No. 1, 109?118 (1967). · Zbl 0173.17806 · doi:10.1137/0704010
[1625] T. Wiberg, ?A combined Lanczos and conjugate gradient method for the eigenvalue problem of large sparse matrices,? Rep. UMINF-42.73 (1973).
[1626] O. B. Widlun, ?On the rate of convergence of an alternating direction implicit method in a noncommutative case,? Math. Comput.,20, No. 96, 500?515 (1966). · doi:10.1090/S0025-5718-1966-0231551-9
[1627] O. B. Widlund, ?On the effects of scaling of the Peace man-Rachford method,? Lect. Notes Math.,109, 113?132 (1969). · Zbl 0185.42101 · doi:10.1007/BFb0060018
[1628] O. B. Widlund, ?On the effects of scaling of the Peaceman-Rachford method,? Math. Comput.,25, No. 113, 33?41 (1971). · Zbl 0225.65044 · doi:10.1090/S0025-5718-1971-0303754-8
[1629] W. Wilhelmi, ?Ein Algorithmus zur Lösung eines inversen Eigenswertproblems,? Z. Angew. Math. Mech.,54, No. 1, 53?55 (1974). · Zbl 0288.65018 · doi:10.1002/zamm.19740540107
[1630] J. H. Wilkinson, ?Note on the quadratic convergence of the cyclic Jacobi process,? Numer. Math.,4, No. 4, 296?300 (1962). · Zbl 0104.34501 · doi:10.1007/BF01386321
[1631] J. H. Wilkinson, ?Householder’s method for symmetric matrices,? Numer. Math.,4, No. 4, 354?361 (1962). · Zbl 0107.34305 · doi:10.1007/BF01386332
[1632] J. H. Wilkinson, ?Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection,? Numer. Math.,4, No. 4, 362?367 (1962). · Zbl 0107.34306 · doi:10.1007/BF01386333
[1633] J. H. Wilkinson, ?Calculation of the eigenvectors of a symmetric tridiagonal matrix by inverse iteration,? Numer. Math.,4, No. 4, 368?376 (1962). · Zbl 0107.34307 · doi:10.1007/BF01386334
[1634] J. H. Wilkinson, ?Errors in large-scale numerical problems,? Comput. Bull.,6, No. 4, 124?125 (1963).
[1635] J. H. Wilkinson, Rounding Errors in Algebraic Processes, H. M. Stat. Off., London (1963), Chap. VI. · Zbl 1041.65502
[1636] J. H. Wilkinson, ?Plane rotations in floating-point arithmetic,? Proc. Sympos. Appl. Math., Vol. 15, Am. Math. Soc., Providence, Rhode Island (1963), pp. 185?198. · Zbl 0131.34002
[1637] J. H. Wilkinson, ?Convergence of the LR, QR and related algorithms,? Comput. J.,8, No. 1, 77?84 (1965). · Zbl 0135.37602 · doi:10.1093/comjnl/8.1.77
[1638] J. H. Wilkinson, ?The QR algorithm for real symmetric matrices with multiple eigenvalues,? Comput. J.,8, No. 1, 85?87 (1965). · Zbl 0135.17802 · doi:10.1093/comjnl/8.1.85
[1639] J. H. Wilkinson, ?Error analysis of transformations based on the use of matrices of the form I-2 WW,? in: Errors in Digital Computation, Vol. 2, Wiley, New York-London-Sydney (1965), pp. 77, 101. · Zbl 0252.65030
[1640] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford (1965), Chap. XVIII. · Zbl 0258.65037
[1641] J. H. Wilkinson, ?Calculation of eigensystems of matrices,? in: Numerical Analysis, An Introduction, Thompson Book Co., Washington, D. C. (1966), pp. 27?62.
[1642] J. H. Wilkinson, ?The solution of ill-conditioned linear equations,? in: Math. Methods for Digital Computers, Vol. 2, 2nd Ed., Wiley, New York-London-Sydney (1967), pp. 65?93.
[1643] J. H. Wilkinson, ?A survey of error analysis of matrix algorithms,? Apl. Mat.,13, No. 1, 93?102 (1968). · Zbl 0153.46104
[1644] J. H. Wilkinson, ?A priori error analysis of algebraic processes,? Tr. Mezhdunar. Kongr. Mat., Moskva, 1966, Mir, Moscow (1968). · Zbl 0197.13301
[1645] J. H. Wilkinson, ?Almost diagonal matrices with multiple or close eigenvalues,? Linear Algebra Appl.,1, No. 1, 1?12 (1968). · Zbl 0167.30303 · doi:10.1016/0024-3795(68)90042-6
[1646] J. H. Wilkinson, ?Global convergence of tridiagonal QR algorithm with origin shifts,? Linear Algebra Appl.,1, No. 3, 409?420 (1968). · Zbl 0237.65029 · doi:10.1016/0024-3795(68)90017-7
[1647] J. H. Wilkinson, ?The basics of error analysis of matrix processes,? Colloq. Int. Centre Nat. Rech. Scient., No. 165, 127?133 (1968).
[1648] J. H. Wilkinson, ?Global convergence of QR algorithm,? Proc. IFIP Congr. 68, Edinburgh, 1968, Vol. 1: Mathematics, Software, North-Holland, Amsterdam (1969), pp. 130?133.
[1649] J. H. Wilkinson, ?Some comments from a numerical analyst,? J. Assoc. Comput. Mach.,18, 137?147 (1971). · Zbl 0223.01015 · doi:10.1145/321637.321638
[1650] J. H. Wilkinson, ?Modern error analysis,? SIAM Rev.,13, No. 4, 548?568 (1971). · Zbl 0243.65018 · doi:10.1137/1013095
[1651] J. H. Wilkinson, ?Note on matrices with a very ill-conditioned eigenproblem,? Numer. Math.,19, No. 2, 176?178 (1972). · Zbl 0252.65027 · doi:10.1007/BF01402528
[1652] J. H. Wilkinson, ?Invariant subspaces,? Gatlinburg VI Symposium on Numerical Algebra (Hopfen am See, 1974), München (1974).
[1653] J. H. Wilkinson and C. Reinsch (eds.), Linear Algebra (Grundlehren Math. Wiss. Einzeldarstell., 186), Springer-Verlag, Berlin (1971), Chap. IX.
[1654] L. B. Willner, ?An elimination method for computing the generalized inverse,? Math. Comput.,21, No. 98, 227?229 (1967). · Zbl 0166.41601 · doi:10.1090/S0025-5718-1967-0223082-8
[1655] R. A. Willoughby (ed.), Proceedings of the Symposium on Sparse Matrices and Their Applications (IBM Watson Res. Center, Yorktown Heights, N.Y., September 9?10, 1968), RAI No. 11707, IBM Corp. Thomas J.Watson Res. Center, Yorktown Heights, N. Y. (1969), Chap. XXII.
[1656] E. L. Wilson, K.-J. Bathe, and W. P. Doherty, ?Direct solution of large systems of linear equations,? Comput. Struct.,4, No. 2, 363?372 (1974). · doi:10.1016/0045-7949(74)90063-7
[1657] S. Winograd, ?A new algorithm for inner product,? IEEE Trans. Comput.,C-17, No. 7, 693?694 (1968). · Zbl 0174.46703 · doi:10.1109/TC.1968.227420
[1658] S. Winograd, ?On the algebraic complexity of inner product,? Linear Algebra Appl.,4, No. 4, 377?379 (1971). · Zbl 0225.68017 · doi:10.1016/0024-3795(71)90008-5
[1659] S. Winograd, ?On multiplication of 2 \(\times\) 2 matrices,? Linear Algebra Appl.,4, No. 4, 381?388 (1971). · Zbl 0225.68018 · doi:10.1016/0024-3795(71)90009-7
[1660] H. W. Wippermann, ?Ein Algol-60 Compiler mit triplex-Zahlen,? Z. Angew. Math. Mech.,47, Sonderh., T76-T79 (1967).
[1661] H. W. Wippermann, ?Realisierung einer Intervall-Arithmetik in einem ALGOL-60 System,? Elektr. Rechenanlagen,9, 224?233 (1967). · Zbl 0168.15502
[1662] P. Wisskirchen, ?Ein Steueruhgsprinzip der Intervallrechnung und dessen Anwendung auf den Gaussschen Algorithmus,? Ber. Ges. Math. Datenverarb., No. 20, 43 (1969).
[1663] P. Wisskirechen, ?Berucksichtigung von Monotonieverhaltnissen bei der intervallarithmetischen Behandlung linearer Gleichungssysteme,? Z. Angew. Math. Mech.,50, Sonderh. 1?4, T79-T80 (1970).
[1664] J. Wolf, ?Méthodes de calcul des valeurs propres d’une matrice quelconque par utilisation de transformations unitaires,? Rev. Franc. Traitement Inf. Chiffres,9, No. 4, 309?326 (1966). · Zbl 0202.43601
[1665] Winifred Wood, ?Note on a modified conjugate gradient method,? Int. J. Numer. Meth. Eng.,7, No. 2, 228?232 (1973). · Zbl 0259.65038 · doi:10.1002/nme.1620070213
[1666] H. Wozniakowski, ?Modification of the alternating direction implicit method and connection with von Neumann’s method,? Zast. Mat.,12, No. 4, 398?411 (1972). · Zbl 0247.65021
[1667] P. Wynn, ?On a device for computing the em (sn) transformation,? Math. Tables Other Aids Comput.,10, No. 54, 91?96 (1956). · doi:10.2307/2002183
[1668] P. Wynn, ?On the convergence and stability of the epsilon algorithm,? SIAM J. Numer. Anal.,3, No. 1, 91?122 (1966). · Zbl 0299.65003 · doi:10.1137/0703007
[1669] Szczepan Wyra, ?Przyblizony sposob wyznaczania macierzy odwrotnych dla pewnej klasy macierzy symetrycznych,? Zesz. Nauk. Politech. Slaskiej, No. 113, 79?90 (1964).
[1670] T. Yamamoto, ?On Lanczos’ algorithm for tridiagonalization,? J. Sci. Hiroshima Univ., Ser. A-1,32, No. 2, 259?284 (1968).
[1671] D. M. Young, ?Convergence properties of the symmetric and unsymmetric successive overrelaxation methods and related methods,? Univ. Texas, Austin, Comput. Center, TNN-96 (1969).
[1672] D. M. Young, ?Convergence properties of the symmetric and unsymmetric successive overrelaxation methods and related methods,? Math. Comput.,24, No. 112, 793?807 (1970). · Zbl 0221.65060 · doi:10.1090/S0025-5718-1970-0281331-4
[1673] D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York-London (1971), Chap. XXIV. · Zbl 0231.65034
[1674] D. M., Young, ?A bounds for the optimum relaxation factor for the successive overrelaxation method,? Numer. Math.,16, No. 5, 408?413 (1971). · Zbl 0195.44903 · doi:10.1007/BF02169150
[1675] D. M. Young, ?Second-degree iterative methods for the solution of large linear systems,? J. Approxim. Theory,5, No. 2, 137?148 (1972). · Zbl 0236.65027 · doi:10.1016/0021-9045(72)90036-6
[1676] D. M. Young, ?On the consistency of linear stationary iterative methods,? SIAM J. Numer. Anal.,9, No. 1, 89?96 (1972). · Zbl 0234.65054 · doi:10.1137/0709010
[1677] D. M. Young, ?Generalizations of property A and consistent ordering,? SIAM J. Numer. Anal.,9, No. 3, 454?463 (1972). · Zbl 0248.65022 · doi:10.1137/0709041
[1678] D. M. Young, ?A survey of modern numerical analysis,? SIAM Rev.,15, No. 2, Part 2, 503?523 (1973). · Zbl 0234.65003 · doi:10.1137/1015069
[1679] D. M. Young, ?Stopping criteria and adaptive parameter determination for iterative methods for solving large linear systems,? Gatlinburg VI Symposium on Numerical Algebra (Hopfen am See, 1974), München (1974).
[1680] D. M. Young and Thurman G. Frank, ?A survey of computer methods for solving elliptic and parabolic partial differential equations,? ICC Bull.,2, No. 1, 3?61 (1963).
[1681] D. M. Young and D. R. Kincaid, ?Norms of the successive overrelaxation method and related methods,? Univ. Texas, Austin, Comput. Center, TNN-94 (1969).
[1682] D. M. Young, M. F. Wheeler, and J. A. Downing, ?On the use of the modified successive overrelaxation method with several relaxation factors,? Proc. IFIP Congr. 65, New York City, 1965, Vol. 1, Spartan Books, Washington, MacMillan, London (1965), pp. 177?182.
[1683] L. J. B. Zeegers, ?Toepassing van vectoren bij net oplossen van n vergelijkinge met n onbekenden,? Tijdschr. Kadaster en Landmeetkunde,80, No. 1, 15?17 (1964).
[1684] Fr. Zelinka, ?Poznamka ke kontrole reseni soustavy linearnich algebraickych rovnic zpetnou substituci,? Apl. Mat.,13, No. 3, 241?247 (1968).
[1685] G. Zielke, ?Inversion of modified symmetric matrices,? J. Assoc. Comput. Mach.,15, No. 3, 402?408 (1968). · Zbl 0162.46703 · doi:10.1145/321466.321472
[1686] G. Zielke, ?Algorithmus 6. Anderung der Inversen einer symmetrischen Matrix bei symmetrischer Zeilen- und Spaltenanderung,? Computing,3, No. 1, 76?77 (1968). · doi:10.1007/BF02238106
[1687] G. Zielke, Numerische Berechnung von Benachbarten Inversen Matrizen und Linearen GleichungsSystemen (Schr. Datenverarb., 2), Vieweg und Sohn, Braunschweig, Friedr. (1970). · Zbl 0191.15703
[1688] G. Zielke, A lgol-Katalog Matrizenrechnung, B. C. Teubner Verlagsgesellschaft, Leipzig (1972).
[1689] K. Zietak, ?On the optimum rational function connected with the ADI-method,? Zast. Mat.,11, 337?352 (1969?1970). · Zbl 0231.65060
[1690] K. Zimmermann, ?Zur Konvergenz eines Jacobiverfahren für gewöhnliche und verallgemeinerte Eigen-wertprobleme,? Diss. Dokt. Math. Eidgenoss. Tech. Hochsch. Zürich (1969).
[1691] J. Zitko, ?Extrapolation of S. O. R. iterations,? Apl. Mat.,19, No. 2, 72?89 (1974). · Zbl 0293.65020
[1692] S. Zlobec, ?On computing the generalized inverse of a linear operator,? Glas. Mat.,2(22), No. 2, 265?271 (1967). · Zbl 0149.35101
[1693] S. Zlobec and M. W. K. Chan, ?The Gauss-Bordering method for matrix inversion,? Z. Angew. Math. Mech.,54, No. 5, 277?279 (1974). · Zbl 0285.65022 · doi:10.1002/zamm.19740540409
[1694] Sh. Zohar, ?Toeplitz matrix inversion: The algorithm of W. F. Trench,? J. Assoc. Comput. Mach.,16, No. 4, 592?601 (1969). · Zbl 0194.18102 · doi:10.1145/321541.321549
[1695] Sh. Zohar, ?The solution of a Toeplitz set of linear equations,? J. Assoc. Comput. Mach.,21, No. 2, 272?276 (1974). · Zbl 0276.65014 · doi:10.1145/321812.321822
[1696] K. Zollenkopf, ?Bi-factorization-basic computational algorithm and programming techniques,? in: Large Sparse Sets of Linear Equations, Academic Press, London-New York (1971), pp. 75?95.
[1697] Z. Zorski, ?Rozwiazywanie symetrycznych ukladow algebraicznych rownan liniowych zmodyfikowana metoda Banachiewicza,? Geod. Kartogr.,20, No. 4, 291?293 (1971).
[1698] R. Zurmühl, ?Bemerkungen zum Verfahren von Hessenberg,? Numer. Math.,4, No. 5, 377?380 (1963). · Zbl 0107.10702 · doi:10.1007/BF01386335
[1699] R. Zurmühl, Matrizen und Ihre Technischen Anwendungen, 4th Impr. Ed., Springer-Verlag, Berlin (1964), Chap. XII. · Zbl 0123.32201
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