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Research Article
DQGMRES: a Direct Quasi-minimal Residual Algorithm Based on Incomplete Orthogonalization
Article first published online: 31 DEC 1998
DOI: 10.1002/(SICI)1099-1506(199607/08)3:4<329::AID-NLA86>3.0.CO;2-8
Copyright © 1996 John Wiley & Sons, Ltd.
1099-1506/asset/cover.gif?v=1&s=4c716168b1bef317e4ae1ebaac712130c9fe6913 "Numerical Linear Algebra with Applications")
Additional Information
How to Cite
Saad, Y. and Wu, K. (1996), DQGMRES: a Direct Quasi-minimal Residual Algorithm Based on Incomplete Orthogonalization. Numerical Linear Algebra with Applications, 3: 329–343. doi: 10.1002/(SICI)1099-1506(199607/08)3:4<329::AID-NLA86>3.0.CO;2-8
Publication History
- Issue published online: 31 DEC 1998
- Article first published online: 31 DEC 1998
- Manuscript Revised: 7 JAN 1996
- Manuscript Received: 1 JAN 1995
Funded by
- DARPA
- National Science Foundation. Grant Numbers: NIST 60NANB2D1272, NSF/CCR-9214116
- Abstract
- References
- Cited By
Keywords:
- iterative methods;
- GMRES;
- Krylov methods;
- incomplete orthogonalization;
- quasi-minimization
Abstract
We describe a Krylov subspace technique, based on incomplete orthogonalization of the Krylov vectors, which can be considered as a truncated version of GMRES. Unlike GMRES(m), the restarted version of GMRES, the new method does not require restarting. Like GMRES, it does not break down. Numerical experiments show that DQGMRES(k) often performs as well as the restarted GMRES using a subspace of dimension m=2k. In addition, the algorithm is flexible to variable preconditioning, i.e., it can accommodate variations in the preconditioner at every step. In particular, this feature allows the use of any iterative solver as a right-preconditioner for DQGMRES(k). This inner-outer iterative combination often results in a robust approach for solving indefinite non-Hermitian linear systems.