Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 670, Issue -, Pages 42-67Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2023.04.003
Keywords
Matrix polynomial; Eigenvalue; Stability; Polarisation operator; Multivariate polynomial
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The paper presents methods for eigenvalue localization of regular matrix polynomials, with a focus on investigating the stability of matrix polynomials. A stronger notion of hyperstability is introduced and discussed extensively. Matrix versions of the Gauss-Lucas theorem and Szasz inequality are demonstrated. Tools for studying (hyper)stability using multivariate complex analysis methods are provided. Several second- and third-order matrix polynomials with specific semi-definiteness assumptions on coefficients are proven to be stable.
The paper presents methods for the eigenvalue localisation of regular matrix polynomials, in particular, the stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix versions of the Gauss-Lucas theorem and Szasz inequality are shown. Further, tools for investigating (hyper) -stability by multivariate complex analysis methods are provid-ed. Several seconds-and third-order matrix polynomials with particular semi-definiteness assumptions on coefficients are shown to be stable.(c) 2023 Elsevier Inc. All rights reserved.
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