A numerical method on the mixed solution of matrix equation ∑i=1tAiXiBi=E with sub-matrix constraints and its application

Highlights：

• In this paper, we proposed an algorithm to solve mixed solutions of the matrix Equation ∑i=1tAiXiBi=E with sub-matrix constraints. We also prove that the iterative solution sequence generated by the algorithm is convergent. Moreover, for a given matrix, its best approximation is obtained, which is the mixed solution of the matrix equation with sub-matrix constraints. Finally, a large number of numerical experiments are carried out, and results show that the algorithm is effective not only in image restoration, but also in the general case, for both small-scale and large-scale matrices. The work belongs to the field of numerical algebra, and has been widely concerned.