Volume 17, Issue 3
Arnoldi Type Algorithms for Large Unsymmetric Multiple Eigenvalue Problems

Zhong Xiao Jia

DOI:

J. Comp. Math., 17 (1999), pp. 257-274

Published online: 1999-06

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  • Abstract

As is well known,solving matrix multiple eigenvalue problems is a very difficult topic. In this paper, Arnoldi type algorithms are proposed for large unsymmetric multiple eigenvalue problems when the matrix A involved is diagonalizable. The theoretical background is established,in which lower and upper error bounds for eigenvectors are new for both Arnoldi's method and a general perturbation problem, and furthermore these bounds are shown to be optimal and they generalize a classical perturbation bound due to W.Kahan in 1967 for A symmetric. The algorithms can adaptively determine the multiplicity of an eigenvalue and a basis of the associated eigenspace. Numerical experiments show reliability of the algorithms.

  • Keywords

Arnolde's process Large unsymmetric matrix

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@Article{JCM-17-257, author = {}, title = {Arnoldi Type Algorithms for Large Unsymmetric Multiple Eigenvalue Problems}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {3}, pages = {257--274}, abstract = { As is well known,solving matrix multiple eigenvalue problems is a very difficult topic. In this paper, Arnoldi type algorithms are proposed for large unsymmetric multiple eigenvalue problems when the matrix A involved is diagonalizable. The theoretical background is established,in which lower and upper error bounds for eigenvectors are new for both Arnoldi's method and a general perturbation problem, and furthermore these bounds are shown to be optimal and they generalize a classical perturbation bound due to W.Kahan in 1967 for A symmetric. The algorithms can adaptively determine the multiplicity of an eigenvalue and a basis of the associated eigenspace. Numerical experiments show reliability of the algorithms. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9100.html} }
TY - JOUR T1 - Arnoldi Type Algorithms for Large Unsymmetric Multiple Eigenvalue Problems JO - Journal of Computational Mathematics VL - 3 SP - 257 EP - 274 PY - 1999 DA - 1999/06 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9100.html KW - Arnolde's process KW - Large unsymmetric matrix AB - As is well known,solving matrix multiple eigenvalue problems is a very difficult topic. In this paper, Arnoldi type algorithms are proposed for large unsymmetric multiple eigenvalue problems when the matrix A involved is diagonalizable. The theoretical background is established,in which lower and upper error bounds for eigenvectors are new for both Arnoldi's method and a general perturbation problem, and furthermore these bounds are shown to be optimal and they generalize a classical perturbation bound due to W.Kahan in 1967 for A symmetric. The algorithms can adaptively determine the multiplicity of an eigenvalue and a basis of the associated eigenspace. Numerical experiments show reliability of the algorithms.
Zhong Xiao Jia. (1970). Arnoldi Type Algorithms for Large Unsymmetric Multiple Eigenvalue Problems. Journal of Computational Mathematics. 17 (3). 257-274. doi:
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