Stability Of Matrix Polynomials In One And Several Variables

Autor:	Szymański, Oskar Jakub, Wojtylak, Michał
Rok vydání:	2022
Předmět:	Mathematics - Complex Variables Mathematics - Numerical Analysis 15A18 15A22 15B57 30C15 32A60
Druh dokumentu:	Working Paper
Popis:	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 Sz\'asz 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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.10509 Zobrazit plný text záznamu View this record from Arxiv