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arXiv · 1612.08369

Refined Bounds on the Number of Distinct Eigenvalues of a Matrix After Perturbation

Yunjie Wang·Gang Wu
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Abstract

The eigenproblem of low-rank updated matrices are of crucial importance in many applications. Recently, an upper bound on the number of distinct eigenvalues of a perturbed matrix was established. The result can be applied to estimate the number of Krylov iterations required for solving a perturbed linear system. In this paper, we revisit this problem and establish some refined bounds. Some {\it a prior} upper bounds that only rely on the information of the matrix in question and the low-rank update are provided. Examples show the superiority of our theoretical results over the existing ones. The number of distinct singular values of a matrix after perturbation is also investigated.

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Yunjie Wang, Gang Wu. 2016-12-26. Refined Bounds on the Number of Distinct Eigenvalues of a Matrix After Perturbation. https://arxiv.org/abs/1612.08369

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