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

65F10Iterative methods for linear systems
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
Full Text: DOI
[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)