The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation
type: Item
instance of: scholarly article
title: The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation
zbMATH Open document ID: 1157.15016
author: Lei Yu
author: Kaiyuan Zhang
author: Zhongke Shi
published in: Journal of Applied Mathematics and Computing
publication date: 2008-10-21T00:00:00Z
review text: Given the linear matrix equation \(A^T XA = B\), by using the generalized singular value decomposition, this paper deals with (1) the necessary and sufficient conditions for the existence of the anti-symmetric ortho-symmetric solution \(X\), and (2) the existence and uniqueness of its optimal approximation \(X^*\) satisfying \(\min_X \| X - X^*\| \). Finally, numerical methods of the optimal approximation are formulated and illustrative numerical experiments are presented.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 5354630
zbMATH Keywords: matrix equation
zbMATH Keywords: anti-symmetric ortho-symmetric solution
zbMATH Keywords: optimal approximation
zbMATH Keywords: singular value decomposition
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: s12190-008-0040-9
OpenAlex ID: W2072216669
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DOI: 10.1007/S12190-008-0040-9
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description: scientific article; zbMATH DE number 5354630