Improved perturbation estimates for the matrix equations \(X \pm A^{*} X^{-1} A=Q\).
type: Item
instance of: scholarly article
title: Improved perturbation estimates for the matrix equations \(X \pm A^{*} X^{-1} A=Q\).
zbMATH Open document ID: 1039.15005
DOI: 10.1016/S0024-3795(03)00424-5
published in: Linear Algebra and its Applications
publication date: 2004-03-14T00:00:00Z
review text: The authors give new and improved perturbation estimates for the solutions of the matrix quadratic equations \(X\pm A^*X^{-1}A=Q\) (\(X\) and \(Q\) are positive definite Hermitian matrices). Some of the estimates depend and some do not depend on the knowledge of the exact solution \(X\). The results are compared with those of \textit{S. F. Xu} [Linear Algebra Appl. 336, 61--70 (2001; Zbl 0992.15013)] and of \textit{A. C. M. Ran} and \textit{M. C. B. Reurings} [Linear Algebra Appl. 346, 15--26 (2002; Zbl 1086.15013)]. The paper contains a presentation of numerical experiments.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 2056680
zbMATH Keywords: perturbation
zbMATH Keywords: matrix equation
zbMATH Keywords: perturbation estimate
zbMATH Keywords: Riccati equation
zbMATH Keywords: positive definite matrix
zbMATH Keywords: numerical experiments
author: V. I. Hasanov
author: Ivan Ganchev Ivanov
author: Frank Uhlig
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
cites work: Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
cites work: Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
cites work: On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
cites work: Scaling of the discrete-time algebraic Riccati equation to enhance stability of the Schur solution method
cites work: Perturbation Theory for Algebraic Riccati Equations
cites work: Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)
description: scientific article; zbMATH DE number 2056680