On positive definite solutions of the matrix equation \(X + A^* X^{-q} A = Q(0 < q \leq 1)\)
type: Item
instance of: scholarly article
title: On positive definite solutions of the matrix equation \(X + A^* X^{-q} A = Q(0 < q \leq 1)\)
zbMATH Open document ID: 1383.15015
author: Tiexiang Li
author: Xiaoyan Yin
author: Sanyang Liu
published in: Taiwanese Journal of Mathematics
publication date: 2013-02-21T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.twjm/1500406740
review text: This paper gives a new sufficient condition for the nonlinear matrix equation \(X+A^{\ast }X^{-q}A=Q\) where \(0<q\leq 1\) to have positive definite solution. The author presents two iterative methods to find the maximal positive definite solution of this equation. Applying the theory of condition number developed by \textit{J. R. Rice} [SIAM J. Numer. Anal. 3, 287--310 (1966; Zbl 0143.37101)], the author gives an explicit expression of the condition number of the maximal positive definite solution. The theoretical results are also illustrated by numerical examples.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6137974
zbMATH Keywords: nonlinear matrix equation
zbMATH Keywords: positive definite solution
zbMATH Keywords: condition number
MaRDI profile type: Publication
OpenAlex ID: W4230271915
DOI: 10.11650/TWJM/1500406740
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description: scientific article; zbMATH DE number 6137974