Iterative positive definite solutions of the two nonlinear matrix equations \(X \pm A^{T}X^{-2} A =I \)
type: Item
instance of: scholarly article
title: Iterative positive definite solutions of the two nonlinear matrix equations \(X \pm A^{T}X^{-2} A =I \)
zbMATH Open document ID: 1072.65065
author: Mohamed A. Ramadan
author: Naglaa M. El-Shazly
author: Talaat S. El Danaf
published in: Applied Mathematics and Computation
publication date: 2005-05-04T00:00:00Z
review text: Consider the matrix equation \(X + \varepsilon A^\top X^{-2}A= I\) in \(\mathbb{R}^{n\times n}\), where \(\varepsilon= \pm1\). The iteration scheme \(X_{k+1}= I -\varepsilon A^\top X^{-2}_k A\), \(X_0= \alpha I\), \(\alpha> 0\), for finding the positive definite solution is justified under certain restrictions on the coefficient matrix \(A\).
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 2165269
zbMATH Keywords: iteration schemes
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
full work available at URL: j.amc.2004.04.080
OpenAlex ID: W2048827285
cites work: Ladder networks, fixpoints, and the geometric mean
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cites work: On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
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DOI: 10.1016/J.AMC.2004.04.080
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description: scientific article; zbMATH DE number 2165269