On the spectrum of a nonlinear two parameter matrix eigenvalue problem

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Abstract

We consider the nonlinear two parameter eigenvalue problem (Tp − λ1Ap1 − λ2Ap2 − λ1λ2Ap3)vp = 0, where λ1, λ2 ∈C; Tp, Apk (p = 1, 2;k = 1, 2, 3) are matrices. Bounds for the spectral radius of that problem are suggested. Our main tool is the recent norm estimates for the resolvent of an operator on the tensor product of Euclidean spaces. In addition, we investigate perturbations of the considered problem and derive a Gershgorin type bounds for the spectrum. It is shown that the main result of the paper is sharp.

Original languageEnglish
Title of host publicationSpringer Optimization and Its Applications
PublisherSpringer International Publishing
Pages387-402
Number of pages16
DOIs
StatePublished - 1 Jan 2018

Publication series

NameSpringer Optimization and Its Applications
Volume134
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

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