(untitled) (Journal of Computational Mathematics, 2021)
The necessary and sufficient conditions for the existence of and the expressions for the bisymmetric solutions of the matrix equations (I) A_1X_1B_1+A_2X_2B_2+…+A_kX_kB_k=D, (II) A_1XB_1+A_2XB_2+…+A_kXB_k=D and (III) (A_1XB_1, A_2XB_2, ··· , A_kXB_k) = (D_1, D_2, ··· , D_k) are derived by using Kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given. Numerical methods and numerical experiments of finding the nearest solutions are also provided.