The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
GMRES with Deflated Restarting
Abstract
A modification is given of the GMRES iterative method for nonsymmetric systems of linear equations. The new method deflates eigenvalues using Wu and Simon's thick restarting approach [SIAM J. Matrix Anal. Appl., 22 (2000), pp. 602--616]. It has the efficiency of implicit restarting but is simpler and does not have the same numerical concerns. The deflation of small eigenvalues can greatly improve the convergence of restarted GMRES. Also, it is demonstrated that using harmonic Ritz vectors is important because then the whole subspace is a Krylov subspace that contains certain important smaller subspaces.
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Cites
Iterative Methods for Sparse Linear Systems
Saad, Y. (2003) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718003 · Cited by 13,790
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
Saad, Y., & Schultz, M. H. (1986) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0907058 · Cited by 11,154
van der Vorst, H. A. (1992) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0913035 · Cited by 5,308
The Symmetric Eigenvalue Problem
Parlett, B. N. (1998) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971163 · Cited by 3,192
Davidson, E. R. (1975) · Journal of Computational Physics · doi:10.1016/0021-9991(75)90065-0 · Cited by 2,517
Numerical Methods for Large Eigenvalue Problems: Revised Edition
Saad, Y. (2011) · doi:10.1137/1.9781611970739 · Cited by 2,364
The principle of minimized iterations in the solution of the matrix eigenvalue problem
Arnoldi, W. E. (1951) · Quarterly of Applied Mathematics · doi:10.1090/qam/42792 · Cited by 1,818
A Flexible Inner-Outer Preconditioned GMRES Algorithm
Saad, Y. (1993) · SIAM Journal on Scientific Computing · doi:10.1137/0914028 · Cited by 1,445
Implicit Application of Polynomial Filters in a k -Step Arnoldi Method
Sorensen, D. C. (1992) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/0613025 · Cited by 1,111
QMR: a quasi-minimal residual method for non-Hermitian linear systems
Freund, R. W., & Nachtigal, N. M. (1991) · Numerische Mathematik · doi:10.1007/bf01385726 · Cited by 979
Cited by
Recent computational developments in Krylov subspace methods for linear systems
Simoncini, V., & Szyld, D. B. (2007) · Numerical Linear Algebra with Applications · doi:10.1002/nla.499 · Cited by 375
Metadata
- Authors
- Morgan, R. B.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2002-01
- Volume
- 24
- Issue
- 1
- Pages
- 20-37
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2052579356
- Cited by
- 289
- References
- 27
- FWCI
- 9.86
- Type
- journal article
- Language
- en
- Open access
- closed
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