Positive definite solution of the matrix equation \(X=Q+A^{H}(I\otimes X-C)^{\delta}A\)
type: Item
instance of: scholarly article
title: Positive definite solution of the matrix equation \(X=Q+A^{H}(I\otimes X-C)^{\delta}A\)
zbMATH Open document ID: 1214.15011
published in: Numerical Algorithms
publication date: 2011-03-31T00:00:00Z
review text: The authors consider the nonlinear matrix equation \(X=Q+A^H(I \otimes X - C)^{\delta}A\), \((\delta = -1\) or \(0 < |\delta| < 1)\), where \(Q\) is an \(n \times n\) positive definite matrix, \(C\) is an \(mn \times mn\) positive semidefinite matrix, \(I\) is the \(m \times m\) identity matrix, and \(A\) is an arbitrary \(mn \times n\) matrix. Under the assumption that \(I \otimes Q > C\), they prove the existence and uniqueness of its positive definite solution which is contained in the set \(\{ X \mid I \otimes X > C \}\).
reviewed by: Constantin Popa
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 5872582
zbMATH Keywords: nonlinear matrix equation
zbMATH Keywords: Hermitian positive definite solution
zbMATH Keywords: Kronecker product
zbMATH Keywords: normal cone
zbMATH Keywords: monotonic operator
author: Guozhu Yao
author: Anping Liao
author: Xuefeng Duan
MaRDI profile type: Publication
full work available at URL: s11075-010-9386-9
OpenAlex ID: W2118293075
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DOI: 10.1007/S11075-010-9386-9
description: scientific article; zbMATH DE number 5872582