Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix
type: Item
instance of: scholarly article
title: Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix
zbMATH Open document ID: 0713.15005
DOI: 10.1016/0024-3795(90)90267-G
author: Rajendra Bhatia
author: Ludwig Elsner
author: Gerd M. Krause
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: The authors derive some new bounds for the distance between the roots of two polynomials in terms of their coefficients. The argument used in the proof of this result is then utilized to obtain bounds for the distance between the eigenvalues of two matrices in terms of the operator norm of their difference.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 4173153
zbMATH Keywords: zeros of polynomials
zbMATH Keywords: operator norms
zbMATH Keywords: spectral norm
zbMATH Keywords: distance
zbMATH Keywords: eigenvalues
reviewed by: George Phillip Barker
MaRDI profile type: Publication
cites work: Q3996765
cites work: On the rate of change of spectra of operators. II
cites work: Variation of symmetric tensor powers and permanents
cites work: Variation of Grassmann powers and spectra
cites work: On the rate of change of spectra of operators
cites work: On the variation of the spectra of matrices
cites work: An optimal bound for the spectral variation of two matrices
cites work: A note on the variation of permanents
cites work: Variation of tensor powers and spectrat
cites work: Q5528098
cites work: Permanental polynomials of graphs
cites work: Q4060241
cites work: Improving spectral-variation bounds with Chebyshev polynomials
cites work: Q5583224
Wikidata QID: Q127220109
description: scientific article; zbMATH DE number 4173153