An efficient algorithm for the generalized centro-symmetric solution of matrix equation A X B=C

In this paper, an iterative algorithm is constructed for solving linear matrix equation AXB = C over generalized centro-symmetric matrix X. We show that, by this algorithm, a solution or the least-norm solution of the matrix equation AXB = C can be obtained within finite iteration steps in the absence of roundoff errors; we also obtain the optimal approximation solution to a given matrix X-0 in the solution set of which. In addition, given numerical examples show that the iterative method is efficient.