On equations that are equivalent to the nonlinear matrix equation \(X+A^{*}X ^{-\alpha}A=Q\)
type: Item
instance of: scholarly article
title: On equations that are equivalent to the nonlinear matrix equation \(X+A^{*}X ^{-\alpha}A=Q\)
zbMATH Open document ID: 1200.65033
author: Xing Tao Wang
author: Yuan Min Li
published in: Journal of Computational and Applied Mathematics
publication date: 2010-06-22T00:00:00Z
review text: The authors consider the following nonlinear matrix equations \[ X^{-1}+A^*X^{\alpha}A=Q\quad (0<\alpha\leq 1)\tag{1} \] and \[ X^{-1}+(AXA^*)^{1/\alpha}=Q\quad (1<\alpha),\tag{2} \] where \(A\) is a nonsingular matrix, \(A^*\) is the conjugate transpose of \(A\), and \(Q\) is an Hermitian positive definite matrix. Necessary and sufficient conditions for the existence of a positive definite solution of Equations (1) and (2) are presented, respectively. In the process of proving the main results, the authors obtain two iterative algorithms and derive error estimates. Finally, three numerical examples are given to demonstrate that these algorithms are applicable.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 5724563
zbMATH Keywords: nonlinear matrix equation
zbMATH Keywords: iterative algorithm
zbMATH Keywords: positive definite solution
zbMATH Keywords: error estimates
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2010.03.004
OpenAlex ID: W2087506994
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DOI: 10.1016/J.CAM.2010.03.004
description: scientific article; zbMATH DE number 5724563