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GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
Abstract
We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an $l_2 $-orthogonal basis of Krylov subspaces. It can be considered as a generalization of Paige and Saunders’ MINRES algorithm and is theoretically equivalent to the Generalized Conjugate Residual (GCR) method and to ORTHODIR. The new algorithm presents several advantages over GCR and ORTHODIR.
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Cited by
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Metadata
- Authors
- Saad, Y., & Schultz, M. H.
- Venue
- SIAM Journal on Scientific and Statistical Computing
- Published
- 1986-07
- Volume
- 7
- Issue
- 3
- Pages
- 856-869
- ISSN
- 0196-5204 (ISSN-L)
- 2168-3417
- OpenAlex
- W2140153041
- Cited by
- 11,154
- References
- 0
- FWCI
- 30.54
- Type
- journal article
- Language
- en
- Open access
- closed
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- Saad, Y., & Schultz, M. H. (1986). GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM Journal on Scientific and Statistical Computing. https://doi.org/10.1137/0907058
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