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Computational Variants of the Lanczos Method for the Eigenproblem
Abstract
The Lanczos process is theoretically ideal for finding several extreme eigenvalues of large sparse symmetric matrices, but because of loss of orthogonality in practice it has largely been ignored, or used with re-orthogonalization. Here it is shown that it can still be an extremely efficient and accurate algorithm if used in an iterative manner. An error analysis is given showing the most accurate algorithms, and the conclusions are supported by computational results.
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Citations
Cited by
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
Solution of Sparse Indefinite Systems of Linear Equations
Paige, C. C., & Saunders, M. A. (1975) · SIAM Journal on Numerical Analysis · doi:10.1137/0712047 · Cited by 1,620
Self-citationThe Lanczos algorithm with selective orthogonalization
Parlett, B. N., & Scott, D. S. (1979) · Mathematics of Computation · doi:10.1090/s0025-5718-1979-0514820-3 · Cited by 403
Non-Hermitian electronic theory and applications to clusters
Santra, R., & Cederbaum, L. S. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00143-6 · Cited by 290
Self-Adapting Linear Algebra Algorithms and Software
Demmel, J., Dongarra, J., Eijkhout, V., Fuentes, E., Petitet, A., Vuduc, R., Whaley, R. C., & Yelick, K. (2005) · Proceedings of the IEEE · doi:10.1109/jproc.2004.840848 · Cited by 204
Metadata
- Authors
- PAIGE, C. C.
- Venue
- IMA Journal of Applied Mathematics
- Publisher
- Oxford University Press (OUP)
- Published
- 1972
- Volume
- 10
- Issue
- 3
- Pages
- 373-381
- ISSN
- 0272-4960 (ISSN-L)
- 1464-3634
- OpenAlex
- W2009737642
- Cited by
- 408
- References
- 0
- FWCI
- 4.46
- Type
- journal article
- Language
- en
- Open access
- closed
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