The Jacobi and Gauss–Seidel-type iteration methods for the matrix equation AXB=CAXB=C

In this paper, the Jacobi and Gauss–Seidel-type iteration methods are proposed for solving the matrix equation AXB=C,AXB=C, which are based on the splitting schemes of the matrices A and B. The convergence and computational cost of these iteration methods are discussed. Furthermore, we give the preconditioned Jacobi and Gauss–Seidel-type iteration methods. Numerical examples are given to demonstrate the efficiency of these methods proposed in this paper.