A relative perturbation bound for positive definite matrices
type: Item
instance of: scholarly article
title: A relative perturbation bound for positive definite matrices
zbMATH Open document ID: 0887.15016
DOI: 10.1016/S0024-3795(97)00248-6
author: Roy Mathias
author: Krešimir Veselić
published in: Linear Algebra and its Applications
publication date: 1998-01-26T00:00:00Z
review text: The author gives an asymptotically sharp bound on the angles between perturbed and unperturbed eigenvectors of a symmetrically perturbed symmetric positive definite matrix. The estimate implies also a bound on the perturbation of the eigenvectors. The proof is surpassingly simple. (There is an unpleasant misprint in the statement of Theorem 1 where ``+'' in equation (2) should be replaced by ``-'').
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1109506
zbMATH Keywords: perturbation bound
zbMATH Keywords: eigenvectors
zbMATH Keywords: symmetric positive definite matrix
reviewed by: Z. Dostál
MaRDI profile type: Publication
cites work: Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices
cites work: Jacobi’s Method is More Accurate than QR
cites work: Q4327451
cites work: Relative Perturbation Techniques for Singular Value Problems
cites work: Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations
cites work: Spectral Perturbation Bounds for Positive Definite Matrices
cites work: A Bound for the Matrix Square Root with Application to Eigenvector Perturbation
cites work: Perturbations of the eigenprojections of a factorized Hermitian matrix
cites work: Condition numbers and equilibration of matrices
cites work: Floating-point perturbations of Hermitian matrices
full work available at URL: s0024-3795(97)00248-6
OpenAlex ID: W2064549639
Wikidata QID: Q127064035
description: scientific article; zbMATH DE number 1109506