Iterative algorithms for solving the matrix equation AXB + CXTD = E

In this paper, we propose two iterative algorithms to solve the matrix equation AXB + CXTD = E. The first algorithm is applied when the matrix equation is consistent. In this case, for any (special) initial matrix X1, a solution (the minimal Frobenius norm solution) can be obtained within finite iteration steps in the absence of roundoff errors. The second algorithm is applied when the matrix equation is inconsistent. In this case, for any (special) initial matrix X1, a least squares solution (the minimal Frobenius norm least squares solution) can be obtained within finite iteration steps in the absence of roundoff errors. Some examples verify the efficiency of these algorithms.