Stability Of Matrix Polynomials In One And Several Variables
Complex Variables
2022-05-18 v3 Numerical Analysis
Numerical Analysis
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 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.
Cite
@article{arxiv.2203.10509,
title = {Stability Of Matrix Polynomials In One And Several Variables},
author = {Oskar Jakub Szymański and Michał Wojtylak},
journal= {arXiv preprint arXiv:2203.10509},
year = {2022}
}
Comments
20 pages