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Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations. (English) Zbl 0439.65020

MSC:
65F10Iterative methods for linear systems
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
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Full Text: DOI
References:
[1] Hestenes, M. R.; Stiefel, E.: Method of conjugate gradients for solving linear systems. J. res. Nat. bur. Standards, No. No. 49, 409-436 (1952) · Zbl 0048.09901
[2] Lanczos, C.: Solution of the systems of linear equations by minimized operations. J. res. Nat. bur. Standards, No. No. 49, 33-53 (1952)
[3] Hestenes, M. R.: The conjugate gradient method for solving linear systems. Proceedings of the symposium on applied mathematics 6, 83-102 (1956) · Zbl 0072.14102
[4] Reid, J. K.: On the method of conjugate gradients for the solution of large sparse systems of linear equations. Proceedings of the conference on large sparse sets of linear equations, 231-254 (1971)
[5] Axelsson, O.: A generalized SSOR method. Nordisk tidskr. Informationsbehandling (BIT) 13, 443-467 (1972) · Zbl 0256.65046
[6] Axelsson, O.: On preconditioning and convergence acceleration in sparse matrix problems. Cern 74-10 (1974) · Zbl 0354.65020
[7] Axelsson, O.: A class of iterative methods for finite element equations. Computer methods in applied mechanics and engineering 9, 123-137 (1976) · Zbl 0334.65028
[8] Axelsson, O.: Solution of linear systems of equations: iterative methods. Sparse matrix techniques (1976) · Zbl 0334.65028
[9] Björck, å.; Elfving, T.: Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations. Report LITH-MAT-R-1977 (1977) · Zbl 0409.65022
[10] Nashed, M. Z.: Generalized inverses, normal solvability and iteration for singular operator equations. Nonlinear functional analysis and applications (1971) · Zbl 0236.41015
[11] Fridman, V. M.: New methods for solving linear operator equations. Dokl. akad. Nauk. SSSR 128, No. 3, 482-484 (1959) · Zbl 0086.32401
[12] Faddeev, D. K.; Faddeeva, V. N.: Computational methods of linear algebra. (1963) · Zbl 0112.07503
[13] Björck, å.: Methods for sparse linear least squares problems. Sparse matrix computations (1976) · Zbl 0351.65004
[14] Elfving, T.: On computing generalized solutions of sparse linear systems with application to some reconstruction problems. Linköping studies in science and technology (1978)
[15] Craig, E. J.: The N-step iteration procedure. J. mathematical phys. 34, 65-73 (1955) · Zbl 0065.10901
[16] O. Axelsson, A generalized conjugate direction method, in preparation. · Zbl 0421.65023
[17] Concus, P.; Golub, G. H.: A generalized conjugate gradient method for nonsymmetric systems of linear equations. Lecture notes in economics and mathematical systems 134 (Dec. 1975)
[18] Widlund, O.: A Lanczos method for a class of nonsymmetric systems of linear equations. SIAM J. Numer. anal. 15, 801-812 (1978) · Zbl 0398.65030
[19] Axelsson, O.; Gustafsson, I.: A modified upwind scheme for convective transport equations and the use of a conjugate gradient method for the solution of non-symmetric systems of eq uations. J. inst. Math. appl. 23, 321-337 (1977) · Zbl 0427.65079
[20] Gustafsson, I.: A class of first-order factorization methods. Nordisk tidskr. Informationsbehandling (BIT) 18, 142-156 (1978) · Zbl 0386.65006
[21] Vinsome, P. K. W.: Orthomin, an iterative method for solving sparse sets of simultaneous linear equations. Society of petroleum engineers of AIME (1976)