global conjugate gradient method for solving large general sylvester matrix equation
چکیده
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.