Document Type : Research Paper
Department of Mathematics and Computer Science, Shahid Bahonar University of Kerman, P.O.Box 761691, Kerman, Iran
In this paper, we study convergence behavior of the global FOM (Gl-FOM) and global GMRES (Gl-GMRES) methods for solving the matrix equation $AXB=C$ where $A$ and $B$ are symmetric positive definite (SPD). We present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual. In particular, the obtained upper bounds for the Gl-FOM method help us to predict the behavior of the Frobenius norm of the Gl-FOM residual. We also explore the worst-case convergence behavior of these methods. Finally, some numerical experiments are given to show the performance of the theoretical results.