The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
Abstract
n this paper we propose a new method for the iterative computation of a few of the extremal. eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi’s approach, combined with Davidson’s method, leads to a new method that has improved convergence properties and that may be used for general matrices. We also propose a variant of the new method that may be useful for the computation of nonextremal eigenvalues as well.
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Citations
Cites
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Numerical Methods for Large Eigenvalue Problems: Revised Edition
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The principle of minimized iterations in the solution of the matrix eigenvalue problem
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Approximate solutions and eigenvalue bounds from Krylov subspaces
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Self-citationJacobi, C. G. J. (1846) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.1846.30.51 · Cited by 255
Computing interior eigenvalues of large matrices
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The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323
The Geometry of Algorithms with Orthogonality Constraints
Edelman, A., Arias, T. A., & Smith, S. T. (1998) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479895290954 · Cited by 2,685
Singular Vectors, Metrics, and Adaptive Observations
Palmer, T. N., Gelaro, R., Barkmeijer, J., & Buizza, R. (1998) · Journal of the Atmospheric Sciences · doi:10.1175/1520-0469(1998)055<0633:svmaao>2.0.co;2 · Cited by 477
Eigenvalue computation in the 20th century
Golub, G. H., & van der Vorst, H. A. (2000) · Journal of Computational and Applied Mathematics · doi:10.1016/s0377-0427(00)00413-1 · Cited by 388
Self-citationThick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
Wu, K., & Simon, H. (2000) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479898334605 · Cited by 306
Metadata
- Authors
- G. Sleijpen, G. L., & Van der Vorst, H. A.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 1996-04
- Volume
- 17
- Issue
- 2
- Pages
- 401-425
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2086160340
- Cited by
- 848
- References
- 17
- FWCI
- 34.53
- Type
- journal article
- Language
- en
- Open access
- closed
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- G. Sleijpen, G. L., & Van der Vorst, H. A. (1996). A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems. SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/s0895479894270427
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
