@Article{JCM-17-257, author = {Jia , Zhong-Xiao}, 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} }