Perturbation analysis for solutions of \(X \pm A^{\ast}X^{-n} A = Q\)
type: Item
instance of: scholarly article
title: Perturbation analysis for solutions of \(X \pm A^{\ast}X^{-n} A = Q\)
zbMATH Open document ID: 1076.15015
author: Xianqiang Yang
published in: Linear Algebra and its Applications
publication date: 2005-02-23T00:00:00Z
review text: The paper is devoted to the properties of positive definite solutions of the nonlinear matrix equations: \[ X + A^*X^{(-n)}A = Q \] and \[ X - A^*X^{(-n)}A = Q, \] where \(A, Q\) are complex \(m \times m\) matrices, \(Q\) is a positive definite matrix, and \(n\) is a natural number. New, more effective perturbation estimates for a positive definite solution are proposed. The topic has been previously introduced by the author and \textit{V. I. Hasanov} in [Appl. Math. Comput. 156, 513--525 (2004; Zbl 1063.15012)], and in [Mathematics and Education in Mathematics, Proceedings 32nd Spring Conference of the Union of Bulgarian Mathematicians, 258--262 (2003)]. The new bounds are compared with earlier results, and are summarized in a table. Some advantages are pointed out. For the numerical results the computer system MATLAB has been used.
reviewed by: Daniela B. Nikolova
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 2137804
zbMATH Keywords: nonlinear matrix equation
zbMATH Keywords: positive definite solution
zbMATH Keywords: perturbation bound
zbMATH Keywords: numerical results
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: j.laa.2004.08.017
OpenAlex ID: W2093353166
cites work: Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\). II
cites work: Solutions and perturbation estimates for the matrix equations \(X\pm A^*X^{-n}A=Q\)
cites work: Improved perturbation estimates for the matrix equations \(X \pm A^{*} X^{-1} A=Q\).
cites work: On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
cites work: Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)
cites work: On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
DOI: 10.1016/J.LAA.2004.08.017
description: scientific article; zbMATH DE number 2137804