Computational methods for large eigenvalue problems (Q2776686)
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scientific article; zbMATH DE number 1714788
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Computational methods for large eigenvalue problems |
scientific article; zbMATH DE number 1714788 |
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11 January 2004
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eigenvalues
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Krylov subspaces
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Lanczos and Arnoldi methods
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large matrices
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survey article
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Jacobi Davidson algorithm
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harmonic Ritz values
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Jacobi algorithm
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polynomial eigenproblems
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homotopy algorithms
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numerical tests
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0.97386956
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0.97386956
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0.97386956
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0.9452026
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0.9425222
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0.9414748
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0.93330616
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0.92591566
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Computational methods for large eigenvalue problems (English)
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A comprehensive review of numerical algorithms for computing eigenvalues of large matrices is given. It starts with a historic perspective, where early developments are put in context with what is known today. It then contains chapters on basic theory, including canonical forms and perturbation theorems, the Jacobi algorithm and transformation methods for the complete eigenproblem. The main emphasis is given to properties of Krylov subspaces and their use in the Lanczos and Arnoldi methods. One chapter is devoted to the author's own favourite children, the Jacobi Davidson algorithm and the use of harmonic Ritz values.NEWLINENEWLINENEWLINEThe review is concluded with a discussion of generalized eigenproblems, polynomial eigenproblems and homotopy algorithms. The review is illustrated by very readable algorithm descriptions. Several numerical tests are reported. These are accompanied by instructive and well informed discussion and are in many cases prepared specially for this review.NEWLINENEWLINEFor the entire collection see [Zbl 0978.00020].
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