The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
Open accessAbstract
In this paper, we propose a restarted variant of the Lanczos method for symmetric eigenvalue problems named the thick-restart Lanczos method. This new variant is able to retain an arbitrary number of Ritz vectors from the previous iterations with a minimal restarting cost. Since it restarts with Ritz vectors, it is simpler than similar methods, such as the implicitly restarted Lanczos method. We carefully examine the effects of the floating-point round-off errors on stability of the new algorithm and present an implementation of the partial reorthogonalization scheme that guarantees accurate Ritz values with a minimal amount of reorthogonalization. We also show a number of heuristics on deciding which Ritz pairs to save during restart in order to maximize the overall performance of the thick-restart Lanczos method.
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Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
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
The Symmetric Eigenvalue Problem
Parlett, B. N. (1998) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971163 · Cited by 3,192
Lehoucq, R. B., Sorensen, D. C., & Yang, C. (1998) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719628 · Cited by 2,936
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
Applied Numerical Linear Algebra
Demmel, J. W. (1997) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971446 · Cited by 2,299
Applied numerical linear algebra
(1998) · Choice Reviews Online · doi:10.5860/choice.35-3919 · Cited by 2,170
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
Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Vol. I: Theory
Cullum, J. K., & Willoughby, R. A. (2002) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719192 · Cited by 1,291
Cited by
Greenacre, M., Groenen, P. J. F., Hastie, T., D’Enza, A. I., Markos, A., & Tuzhilina, E. (2022) · Nature Reviews Methods Primers · doi:10.1038/s43586-022-00184-w · Cited by 1,773
Metadata
- Authors
- Wu, K., & Simon, H.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 2000-01
- Volume
- 22
- Issue
- 2
- Pages
- 602-616
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W1964217357
- Cited by
- 306
- References
- 31
- FWCI
- 2.25
- Type
- journal article
- Language
- en
- Open access
- green
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