Some new perturbation bounds for the generalized polar decomposition
type: Item
instance of: scholarly article
title: Some new perturbation bounds for the generalized polar decomposition
zbMATH Open document ID: 1067.15017
author: Wen Li
author: Xiao Shan Chen
author: Weiwei Sun
published in: BIT
publication date: 2005-04-07T00:00:00Z
review text: The generalized polar decomposition of an \(m\times n\) complex matrix \(A\) of rank \(r\) is \(A=QH\), where \(Q=U_1V_1^\star\), \(H=V_1\Sigma_1V_1^\star\), and \[ A=U\Sigma V^\star=(U_1,U_2)\begin{pmatrix} \Sigma_1&0\\ 0&0\end{pmatrix} (V_1,V_2)^\star=U_1\Sigma_1V_1^\star, \] \(\Sigma_1=\text{ diag}\,(\sigma_1,\ldots,\sigma_r)\) with \(\sigma_1\geq\sigma_2\geq\cdots\geq\sigma_r>0\). The authors introduce a new measure of perturbation and give formulas for the additive and multiplicative perturbation bounds for the subunitary polar factor \(Q\).
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 2153700
zbMATH Keywords: generalized polar decomposition
zbMATH Keywords: perturbation bound
zbMATH Keywords: subunitary polar factor
MaRDI profile type: Publication
full work available at URL: b:bitn.0000039423.58964.e1
OpenAlex ID: W1985816034
DOI: 10.1023/B:BITN.0000039423.58964.E1
description: scientific article; zbMATH DE number 2153700