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Improvement of the minimal residual method for solving nonsymmetric linear systems. (English) Zbl 1143.65331

Summary: The minimal residual method for solving systems of nonsymmetric equations is improved, a recurrence relation is deduced between the approximate solutions of the systems of linear equations \(Ax=b\), and a more effective method is presented, which can reduce the operational count and the storage.

MSC:

65F10 Iterative numerical methods for linear systems

Software:

LSQR; CRAIG
Full Text: DOI

References:

[1] Saad Y, Schultz M H. A generalized minimal residual method for solving nonsymmetric linear systems [J]. SIAM Journal on Statistic Computing, 1986, 7(3): 856–869. · Zbl 0599.65018 · doi:10.1137/0907058
[2] Jiang Er-xiong. Symmetrical Matrix Computing [M]. Shanghai: Shanghai Science and Technology Press, 1984 (in Chinese).
[3] Paige C C, Saunders M A. LSQR: an algorithm for sparse linear equations and sparse least squares [J]. ACM Transaction on Mathematical Software, 1982, 8(1): 43–71. · Zbl 0478.65016 · doi:10.1145/355984.355989
[4] Jiang Er-xiong. An MRES method by Lanczos process for solving nonsymmetric linear systems [C]//Proceedings of the 97’ International Conference on Numerical Optimization and Numerical Linear Algebra. Beijing: Science Press, 1999, 26–37.
[5] Jbilou K, Messaoudi A, Sadok H. Global FOM and GMRES algorithms for matrix equations [J]. Applied Numerical Mathematics, 1999, 31(1): 49–63. · Zbl 0935.65024 · doi:10.1016/S0168-9274(98)00094-4
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