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Research Article | Open Access

The least-squares solutions of the matrix equation A ∗ X B + B ∗ X ∗ A = D and its optimal approximation

Huiting Zhang1, Yuying Yuan2, Sisi Li1, Yongxin Yuan1( )
School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
Library of Hubei Normal University, Huangshi 435002, China
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Abstract

In this paper, the least-squares solutions to the linear matrix equation A ∗ X B + B ∗ X ∗ A = D are discussed. By using the canonical correlation decomposition (CCD) of a pair of matrices, the general representation of the least-squares solutions to the matrix equation is derived. Moreover, the expression of the solution to the corresponding weighted optimal approximation problem is obtained.

Keywords

matrix equationleast-squares solutioncanonical correlation decompositionweighted optimal approximation
CLC number: 15A09, 15A24

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 3680-3691
DOI: 10.3934/math.2022203

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Zhang H, Yuan Y, Li S, et al. The least-squares solutions of the matrix equation A ∗ X B + B ∗ X ∗ A = D and its optimal approximation. AIMS Mathematics, 2022, 7(3): 3680-3691. https://doi.org/10.3934/math.2022203

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Received: 09 September 2021
Accepted: 25 November 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)