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A parallel projection method for linear algebraic systems. (English) Zbl 0398.65013

MSC:
65F10 Iterative numerical methods for linear systems
65H10 Numerical computation of solutions to systems of equations
65F25 Orthogonalization in numerical linear algebra
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References:
[1] R. P. Brent: Algorithms for minimization without derivatives. Prentice-Hall, Englewood Cliffs, New Jersey) · Zbl 0245.65032
[2] D. Chazan W. L. Miranker: A nongradient and parallel algorithm for unconstrained minimization. SIAM J. Control, 2 (1970), 207-217. · Zbl 0223.65022 · doi:10.1137/0308015
[3] E. Durand: Solution numérique des equations algebraiques II. Masson, Paris)
[4] D. K. Faddeev V. N. Faddeeva: Computational methods of linear algebra. Fizmatgiz, Moscow, (1960)) · Zbl 0094.11005
[5] L. Fox H. D. Huskey J. D. Wilkinson: Notes on the solution of algebraic linear simutaneous equations. Quart. J. Mech. Appl. Math., 1 (1948), 149-173. · Zbl 0033.28503 · doi:10.1093/qjmam/1.1.149
[6] N. Gastinel: Analyse numérique linéaire. Hermann, Paris) · Zbl 0151.21202
[7] D. Goldfarb: Modification methods for inverting matrices and solving systems of linear algebraic equations. Math. of Comp., 26 (1972), 829-852. · Zbl 0268.65026 · doi:10.2307/2005866
[8] M. R. Hestenes E. Stiefel: The method of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards, 49 (1952), 409-436. · Zbl 0048.09901 · doi:10.6028/jres.049.044
[9] A. S. Householder F. L. Bauer: On certain iterative methods for solving linear systems. Numer. Math., 2 (1960), 55-59. · Zbl 0168.13501 · doi:10.1007/BF01386209 · eudml:131444
[10] S. Kaczmarz: Angenäherte Auflösung von Systemen linearen Gleichungen. Bull. Acad. Polon. Sciences et Lettres, A, (1937), 355-357. · Zbl 0017.31703
[11] J. Morris: An escalator process for the solution of linear simultaneous equations. Philos. Mag., 37 (1946), 106-120. · Zbl 0061.27101 · doi:10.1080/14786444608561331
[12] M. J. D. Powell: An efficient method for finding minimum of a function of several variables without calculating derivatives. Comp. J., 7 (1964), 155 -162. · Zbl 0132.11702
[13] E. W. Purcell: The vector method for solving simultaneous linear equations. J. Math. and Phys., 32 (1954), 180-183. · Zbl 0051.35303
[14] F. Sloboda: Parallel method of conjugate directions for minimization. Apl. mat., 20 (1975), 436-446. · Zbl 0326.90050 · eudml:14934
[15] F. Sloboda: Nonlinear iterative methods and parallel computation. Apl. mat., 21 (1976), 252-262. · Zbl 0356.65057 · eudml:14963
[16] F. Sloboda: A conjugate directions method and its application. Proc. of the 8th IFIP Conference on Optimization Techniques, Würzburg, (1977), to appear in Springer Verlag. · Zbl 0372.90106
[17] G. Stewart: Conjugate direction methods for solving systems of linear equations. Numer. Math., 21 (1973), 285-297. · Zbl 0253.65017 · doi:10.1007/BF01436383 · eudml:132235
[18] P. Václavík: Parallel algorithms for solving 3-diagonal systems of linear equations. (Slovak), Thesis, Fac. of Sc., Komenský Univ., Bratislava (1974).
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