Global conjugate gradient method for solving large general Sylvester matrix equation

In this paper, an iterative method is proposed for solving large general Sylvester matrix equation AXB॰=E, where A∈Rn×n , C∈Rn×n , B∈Rs×s and D∈Rs×s are given matrices and X∈Rs×s is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm 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 experi- ments are given to illustrate the efficiency of the method.