Abstract
Let and represent the sets of all η-Hermitian quaternion matrices and η-anti-Hermitian quaternion matrices, respectively. On the basis of the real representation matrix of a quaternion matrix and its particular structure, we convert the least squares problem of the quaternion matrix equation AXB + CY D = E over into the corresponding problem of the real matrix equation over free variables, and then we establish its unique minimal norm least squares solution. Our resulting expressions are expressed only by real matrices, and the algorithm only includes real operations. Consequently, they are very simple and convenient. Compared with the existing method [S.F. Yuan, Q.W. Wang, and X. Zhang, Least-squares problem for the quaternion matrix equation AXB + CYD = E over different constrained matrices, Int. J. Comput. Math. 90 (2013), pp. 565–576], the final two examples show that our method is more efficient and superior.
Acknowledgments
The authors are grateful to the anonymous referees for valuable comments and suggestions, which greatly improve the original manuscript of this paper. The study is supported by the National Natural Science Foundation of China (No. 11801249), and the Scientific Research Foundation of Liaocheng University (No. 318011921).
Disclosure statement
No potential conflict of interest was reported by the author(s).