Open AccessThe least-squares solutions of the matrix equation $ A^{\ast}XB+B^{\ast}X^{\ast}A = D $ and its optimal approximation
Author(s) -
Huiting Zhang,
AUTHOR_ID,
Yuying Yuan,
Sisi Li,
Yongxin Yuan,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022203
Subject(s) - mathematics , least squares function approximation , matrix (chemical analysis) , representation (politics) , mathematical analysis , combinatorics , chemistry , statistics , chromatography , estimator , politics , political science , law
In this paper, the least-squares solutions to the linear matrix equation $ A^{\ast}XB+B^{\ast}X^{\ast}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.