@Article{JCM-17-3,
author = {Zhong-Xiao, Jia},
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 = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {1991-7139},
doi = {https://doi.org/1999-JCM-9100},
url = {https://global-sci.com/article/85619/arnoldi-type-algorithms-for-large-unsymmetric-multiple-eigenvalue-problems}
}