%0 Journal Article %T Global conjugate gradient method for solving large general Sylvester matrix equation %J Journal of Mathematical Modeling %I University of Guilan %Z 2345-394X %A Karimi, Saeed %D 2013 %\ 05/01/2013 %V 1 %N Issue 1 %P 15-27 %! Global conjugate gradient method for solving large general Sylvester matrix equation %R %X In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A \in R^{n\times n}$ , $C \in R^{n\times n}$ , $B \in R^{s\times s}$ and  $D \in R^{s\times s}$ are given matrices and $X \in R^{s\times s}$  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. %U https://jmm.guilan.ac.ir/article_94_1e1d28447d734ae7d2d734743b7e1042.pdf