Containment regions for zeros of polynomials from numerical ranges of companion matrices
type: Item
instance of: scholarly article
title: Containment regions for zeros of polynomials from numerical ranges of companion matrices
zbMATH Open document ID: 1002.15026
DOI: 10.1016/S0024-3795(02)00273-2
author: Hansjörg Linden
published in: Linear Algebra and its Applications
publication date: 2002-08-28T00:00:00Z
review text: The results on containment regions for the numerical range of certain companion matrices (bounded diagonal matrices) of a given polynomial \(P_n(x)=x^n-a_1x^{n-1}-\dots-a_n(a_1,\dots, a_n\in {\mathbb C}\), \(a_n\neq 0\), \(\deg P_n\geq 3\)) are applied to obtain containment regions for the zeros of~\(P_n\). In some cases the obtained regions are better than the known ones, as several examples show.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 1790261
zbMATH Keywords: numerical range
zbMATH Keywords: bordered diagonal matrix
zbMATH Keywords: companion matrix
zbMATH Keywords: zeros of polynomial
zbMATH Keywords: containment regions
reviewed by: A. R. Alimov
MaRDI profile type: Publication
cites work: THE GEOMETRY OF THE HAUSDORFF DOMAIN IN LOCALIZATION PROBLEMS FOR THE SPECTRUM OF ARBITRARY MATRICES
cites work: On the numerical range of tridiagonal operators
cites work: Operator norms as bounds for roots of algebraic equations
cites work: Buzano's Inequality and Bounds for Roots of Algebraic Equations
cites work: Q4040931
cites work: The numerical range of \(3 \times 3\) matrices
cites work: Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices
cites work: Numerical radii of some companion matrices and bounds for the zeros of polynomials
cites work: On Composite Abstract Homogeneous Polynomials
cites work: A bibliography on roots of polynomials
cites work: A supplementary bibliography: on roots of polynomials
cites work: An updated supplementary bibliography on roots of polynomials
cites work: Q4861743
cites work: Q3257783
cites work: Iterative methods for simultaneous inclusion of polynomial zeros
description: scientific article; zbMATH DE number 1790261