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Global conjugate gradient method for solving large general Sylvester matrix equation | ||
| Journal of Mathematical Modeling | ||
| مقاله 2، دوره 1، Issue 1، خرداد 2013، صفحه 15-27 اصل مقاله (174.09 K) | ||
| نوع مقاله: Research Article | ||
| نویسنده | ||
| Saeed Karimi* | ||
| چکیده | ||
| 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. | ||
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