Karimi, S. (2013). Global conjugate gradient method for solving large general Sylvester matrix equation. Journal of Mathematical Modeling, 1(Issue 1), 15-27.

Saeed Karimi. "Global conjugate gradient method for solving large general Sylvester matrix equation". Journal of Mathematical Modeling, 1, Issue 1, 2013, 15-27.

Karimi, S. (2013). 'Global conjugate gradient method for solving large general Sylvester matrix equation', Journal of Mathematical Modeling, 1(Issue 1), pp. 15-27.

Karimi, S. Global conjugate gradient method for solving large general Sylvester matrix equation. Journal of Mathematical Modeling, 2013; 1(Issue 1): 15-27.

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 $A \in R^{n\times n}$ , $C \in R^{n\times n}$ , $B \in R^{s\times s}$ 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.