Relative perturbation bounds for the unitary polar factor
type: Item
instance of: scholarly article
title: Relative perturbation bounds for the unitary polar factor
zbMATH Open document ID: 0871.15018
DOI: 10.1007/BF02510173
author: Ren-Cang Li
published in: BIT
publication date: 1997-04-16T00:00:00Z
review text: For each \(m\times n\) complex (or real) matrix \(B\) \((m\geq n)\) with full column rank we have a unique polar decomposition \(B=QH\), where \(Q\) has orthonormal columns and \(H\) is positive definite. The following problem is discussed: How much may \(Q\) change if \(B\) is perturbed to \(\widetilde B= D^*_1BD_2\), where \(D^*_1\) and \(D_2\) are nonsingular and ``close'' to the identity matrix of the same size. It is shown that the change in \(Q\) is bounded only by the distances of \(D^*_1\) and \(D_2\) to the corresponding identity matrices, but does not depend on the singular values of \(B\).
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 1000364
zbMATH Keywords: relative perturbation bounds
zbMATH Keywords: polar decomposition
zbMATH Keywords: singular values
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1000364