Year: 1999
Author: Zhong-Xiao Jia
Journal of Computational Mathematics, Vol. 17 (1999), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1999-JCM-9100
Journal of Computational Mathematics, Vol. 17 (1999), Iss. 3 : pp. 257–274
Published online: 1999-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Arnoldi's process Large unsymmetric matrix Multiple eigenvalue Diagonalizable Error bounds.