2016/07/04 by Xuefeng Xu, Xu, Xuefeng
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Electromagnetic Scattering and Analysis
paper · pdf · doi:10.48550/arxiv.1607.00766
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.