Stability of matrix polynomials in one and several variables

被引：0

作者：

Szymanski, Oskar Jakub ^{[1
]}

Wojtylak, Michal ^{[1
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 670卷

关键词：

Matrix polynomial; Eigenvalue; Stability; Polarisation operator; Multivariate polynomial; NUMERICAL RANGE; EIGENVALUES; BOUNDS; ROOTS;

D O I：

10.1016/j.laa.2023.04.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：42 / 67

页数：26

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