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 $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  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.