A minimal residual algorithm for the inconsistent matrix equation AXB + CYD = E over anti-symmetric matrices

A minimal residual algorithm based on the idea of the classical CG method for the inconsistent matrix equation AXB + CYD = E is constructed in this paper. By this method, the minimum norm least squares solution for anti-symmetric matrices can be obtained within finite iteration steps by choosing a special kind of initial iteration matrix when the matrix equation AXB + CYD = E is not consistent and an error bound is given. Finally, an example verifies the efficiency of the algorithm.