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The Symmetric Eigenvalue Problem
Abstract
According to Parlett, 'Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts.' Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse.
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Citations
Cited by
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Linear and nonlinear response functions for an exact state and for an MCSCF state
Olsen, J., & Jo/rgensen, P. (1985) · The Journal of Chemical Physics · doi:10.1063/1.448223 · Cited by 1,122
A method for accelerating the molecular dynamics simulation of infrequent events
Voter, A. F. (1997) · The Journal of Chemical Physics · doi:10.1063/1.473503 · Cited by 608
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
Thick-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
- Parlett, B. N.
- Venue
- Society for Industrial and Applied Mathematics eBooks
- Published
- 1998-01
- OpenAlex
- W2059586807
- Cited by
- 3,192
- References
- 0
- FWCI
- 30.75
- Type
- book
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The Symmetric Eigenvalue Problem. https://app.cochat.ai/papers/10.1137/1.9781611971163
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- Parlett, B. N. (1998). The Symmetric Eigenvalue Problem. Society for Industrial and Applied Mathematics eBooks. https://doi.org/10.1137/1.9781611971163
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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.
