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.
Citation: Huiting Zhang, Yuying Yuan, Sisi Li, Yongxin Yuan. The least-squares solutions of the matrix equation $ A^{\ast}XB+B^{\ast}X^{\ast}A = D $ and its optimal approximation[J]. AIMS Mathematics, 2022, 7(3): 3680-3691. doi: 10.3934/math.2022203
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.
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Huiting Zhang, Yuying Yuan, Sisi Li, Yongxin Yuan. The least-squares solutions of the matrix equation $ A^{\ast}XB+B^{\ast}X^{\ast}A = D $ and its optimal approximation[J]. AIMS Mathematics, 2022, 7(3): 3680-3691. doi: 10.3934/math.2022203
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