Stability Of Matrix Polynomials In One And Several Variables

2022/03/20 by Oskar Jakub Szymański, Szymański, Oskar Jakub, Michał Wojtylak +1
Computer Science · Mathematics · Physics and Astronomy · #15A18 #15A22 #15B57 #30C15 #32A60 #Advanced Mathematical Theories and Applications #Advanced Optimization Algorithms Research #Complex Variables (math.CV) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2203.10509

openalex publication_date 2022/03/20 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, 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 Szász inequality are shown. Further, tools for investigating (hyper)stability by multivariate complex analysis methods are provided. Several second- and third-order matrix polynomials with particular semi-definiteness assumptions on coefficients are shown to be stable.

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