An improved upper bound for the number of distinct eigenvalues of a matrix after perturbation
Numerical Analysis
2016-10-18 v2 Spectral Theory
Abstract
An upper bound for the number of distinct eigenvalues of a perturbed matrix has been recently established by P. E. Farrell [1, Theorem 1.3]. The estimate is the central result in Farrell's work and can be applied to estimate the number of Krylov iterations required for solving a perturbed linear system. In this paper, we present an improved upper bound for the number of distinct eigenvalues of a matrix after perturbation. Furthermore, some results based on the improved estimate are presented.
Cite
@article{arxiv.1607.00766,
title = {An improved upper bound for the number of distinct eigenvalues of a matrix after perturbation},
author = {Xuefeng Xu},
journal= {arXiv preprint arXiv:1607.00766},
year = {2016}
}