The least-squares solutions of the matrix equation $ A^{\ast}XB+B^{\ast}X^{\ast}A = D $ and its optimal approximation

Autor: Huiting Zhang, Yuying Yuan, Sisi Li, Yongxin Yuan
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: AIMS Mathematics, Vol 7, Iss 3, Pp 3680-3691 (2022)
Druh dokumentu: article
ISSN: 2473-6988
DOI: 10.3934/math.2022203?viewType=HTML
Popis: 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.
Databáze: Directory of Open Access Journals