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

共 50 条

[21] Random Perturbations of Matrix Polynomials [J].

Pagacz, Patryk ;

Wojtylak, Michal .

JOURNAL OF THEORETICAL PROBABILITY, 2022, 35 (01) :52-88

[22] Random Perturbations of Matrix Polynomials [J].

Patryk Pagacz ;

Michał Wojtylak .

Journal of Theoretical Probability, 2022, 35 :52-88

[23] On the bounds of eigenvalues of matrix polynomials [J].

Shah, W. M. ;

Singh, Sooraj .

JOURNAL OF ANALYSIS, 2023, 31 (01) :821-829

[24] NUMERICAL RANGE OF MATRIX POLYNOMIALS [J].

LI, CK ;

RODMAN, L .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1994, 15 (04) :1256-1265

[25] On the bounds of eigenvalues of matrix polynomials [J].

W. M. Shah ;

Sooraj Singh .

The Journal of Analysis, 2023, 31 :821-829

[26] ON THE LOCATION OF EIGENVALUES OF MATRIX POLYNOMIALS [J].

Cong-Trinh Le ;

Thi-Hoa-Binh Du ;

Tran-Duc Nguyen .

OPERATORS AND MATRICES, 2019, 13 (04) :937-954

[27] Symmetry of the spatial numerical ranges of algebra polynomials and of matrix polynomials [J].

Chryssakis Th. .

Journal of Mathematical Sciences, 1999, 96 (6) :3716-3721

[28] FAST AND BACKWARD STABLE COMPUTATION OF EIGENVALUES AND EIGENVECTORS OF MATRIX POLYNOMIALS [J].

Aurentz, Jared ;

Mach, Thomas ;

Robol, Leonardo ;

Vandebril, Raf ;

Watkins, David S. .

MATHEMATICS OF COMPUTATION, 2019, 88 (315) :313-347

[29] The numerical range of self-adjoint quadratic matrix polynomials [J].

Lancaster, P ;

Psarrakos, P .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2002, 23 (03) :615-631

[30] On matrix integration of matrix polynomials [J].

Szafraniec, FH .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 133 (1-2) :611-621

← 1 2 3 4 5 →