Perturbation analysis of the matrix equation \(X-A^*X^{-p}A=Q\)
type: Item
instance of: scholarly article
title: Perturbation analysis of the matrix equation \(X-A^*X^{-p}A=Q\)
zbMATH Open document ID: 1173.15006
author: Jing Li
author: Yuhai Zhang
published in: Linear Algebra and its Applications
publication date: 2009-09-14T00:00:00Z
review text: The authors consider the matrix equation \(X-A^*X^{-p}A=Q\) with \(0<p\leq 1\), with \(X\), \(A\) and \(Q\) being \(n\times n\)-complex matrices, \(Q\) being positive definite. They prove (using a new method) existence and uniqueness of a positive definite solution \(X\). Except a generalization of known results for arbitrary \(p\in (0,1]\), a sharper perturbation bound and backward error of an approximation of this solution are evaluated. Explicit expressions of the condition number for the unique positive definite solution are obtained. The results are illustrated by numerical examples.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A12
zbMATH DE Number: 5603567
zbMATH Keywords: nonlinear matrix equation
zbMATH Keywords: positive definite solution
zbMATH Keywords: perturbation bound
zbMATH Keywords: condition number
zbMATH Keywords: backward error
zbMATH Keywords: numerical examples
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: j.laa.2009.05.013
OpenAlex ID: W2051155033
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DOI: 10.1016/J.LAA.2009.05.013
description: scientific article; zbMATH DE number 5603567