Alternating direction method for generalized Sylvester matrix equation AXB + CYD = E

This paper presents alternating direction methods of multipliers for finding the solution, the best approximate solution and the nonnegative solution of the generalized Sylvester matrix equation AXB + CYD = E, where A, B, C, D and E are given matrices of suitable sizes. Preliminary convergence properties of the proposed algorithms are given. Numerical experiments show that the proposed algorithms tend to deliver higher quality solutions with less iteration steps and less computing times than recent algorithms on the tested problems.