@article{Zhang2022, 
author = {Huiting Zhang and Yuying Yuan and Sisi Li and Yongxin Yuan},
title = {The least-squares solutions of the matrix equation        A          ∗        X  B  +      B          ∗            X          ∗        A  =  D and its optimal approximation},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {3},
pages = {3680-3691},
keywords = {matrix equation, least-squares solution, canonical correlation decomposition, weighted optimal approximation},
url = {https://www.sciopen.com/article/10.3934/math.2022203},
doi = {10.3934/math.2022203},
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.}
}