×

DFOM algorithm and error analysis for projection methods for solving singular linear system. (English) Zbl 1056.65030

Authors’ summary: The DFOM algorithm is presented. We compare the DGMRES algorithm with the DFOM algorithm by numerical experiments. An error analysis for projection method is also given.

MSC:

65F10 Iterative numerical methods for linear systems

Software:

DGMRES
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arnoldi, W. E., The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. Appl. Math, 9, 17-29 (1951) · Zbl 0042.12801
[2] Ben-Israel, A.; Grevile, T. N.E., Generalized Inverses: Theory and Applications (1974), Wiley: Wiley New York, second ed., Springer-Verlag, New York, 2003
[3] Brown, P. N.; Walker, H. F., GMRES on (nearly) singular systems, SIAM J. Matrix Anal., Appl, 18, 37-51 (1997) · Zbl 0876.65019
[4] Campell, S. L.; Meyer, C. D., Generalized Inverses of Linear Transformations (1979), Pitman: Pitman London
[5] Eiermann, M.; Marek, I.; Niethammer, W., On the solution of singular linear systems of algebra equatons by semiiterative methods, Numer. Math, 53, 265-283 (1988) · Zbl 0655.65049
[6] Freund, R. W.; Hochbruck, M., On the use of two QMR algorithms to solve singular systems and applications in Markov chains modeling, Numer. Linear Algebra App, 1, 403-420 (1994) · Zbl 0840.65021
[7] Hanke, M.; Hochbruck, M., A Chebyshev-like semiiteration for inconsistent linear systems, Electron. Trans. Numer. Anal, 1, 315-339 (1993) · Zbl 0809.65039
[8] Ipsen, I. C.F.; Meyer, C. D., The idea behind Krylov methods, Amer. Math. Monthly, 105, 889-899 (1998) · Zbl 0982.65034
[9] Saad, Y.; Schultz, M. H., A generalized minimal residual algorithm for solving non-symmetric linear systems, SIAM J. Sci. Satist. Comput, 7, 856-869 (1986) · Zbl 0599.65018
[10] Sidi, A., A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular non-symmetric linear systems, Linear Algebra Appl, 298, 99-113 (1999) · Zbl 0983.65054
[11] Sidi, A.; Kluzner, V., A Bi-CG type iterative method for Drazin inverse solution of singular inconsistent non-symmetric linear systems of arbitrary index, Electron. J. Linear Algebra, 6, 72-94 (1999) · Zbl 0965.65064
[12] Sidi, A., DGMRES: a GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems, Linear Algebra Appl, 335, 189-204 (2001) · Zbl 0982.65043
[13] Smoch, L., Some result about GMRES in the singular case, Numer. Algorithms, 22, 193-212 (1999) · Zbl 0945.65027
[14] Wei, Y.; Wu, H., Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index, J. Comput. Appl. Math, 114, 305-318 (2000) · Zbl 0959.65046
[15] J. Zhou, Y. Wei, Stagnation analysis of DGMRES, Appl. Math. Comput., in press; J. Zhou, Y. Wei, Stagnation analysis of DGMRES, Appl. Math. Comput., in press · Zbl 1056.65036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.