Saeed Karimi

In this paper, an iterative method is proposed for solving large general Sylvester matrix equation AXB CXD = E, where A ? Rn×n, C ? Rn×n, B ? Rs×s and D ? Rs×s are given matrices and X ? Rn×s is the unknown matrix. We present a global conjugate gradient (GL-CG) algorithm for solving linear system of equations with multiple right-hand sides. By defining a linear matrix operator and imposing some conditions on this operator, we demonstrate how to employ the GL-CG algorithm for solving large general Sylvester matrix equation. Finally, some numerical experiments are given to illustrate the efficiency of the method.