The least-squares solutions of the matrix equation $ A^{\ast}XB+B^{\ast}X^{\ast}A = D $ and its optimal approximation
oleh: Huiting Zhang, Yuying Yuan, Sisi Li, Yongxin Yuan
| Format: | Article |
|---|---|
| Diterbitkan: | AIMS Press 2022-01-01 |
Deskripsi
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.