Optimal perturbation bounds for the Hermitian eigenvalue problem
type: Item
instance of: scholarly article
title: Optimal perturbation bounds for the Hermitian eigenvalue problem
zbMATH Open document ID: 0957.15015
DOI: 10.1016/S0024-3795(99)00268-2
author: Jesse L. Barlow
author: Ivan Slapničar
published in: Linear Algebra and its Applications
publication date: 2001-03-20T00:00:00Z
review text: This paper looks for optimal error bounds for the relative error of the eigenvalues of \(Hx = \lambda Mx\) for Hermitian matrices \(H\) and \(M\). It extends the theory to the singular case for the generalized eigenvalues that are neither zero nor infinite under the perturbation. The given bounds are optimal, they reflect the structure of the perturbations, and they usually tighten the corresponding global error and conditioning estimates.
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1443441
zbMATH Keywords: eigenvalue perturbation
zbMATH Keywords: relative error bound
zbMATH Keywords: structured perturbation
zbMATH Keywords: Hermitian matrices
zbMATH Keywords: conditioning estimates
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1443441