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

Huiting Zhang | Zendy; Yuying Yuan | Zendy; Sisi Li | Zendy; Yongxin Yuan | Zendy

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

Author(s) -

Huiting Zhang,

Yuying Yuan,

Sisi Li,

Yongxin Yuan

Publication year - 2021

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.

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