Convergence analysis of the global FOM and GMRES methods for solving matrix equations $AXB=C$ with SPD coefficients
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Abstract:
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.
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Journal title
volume 41 issue 4
pages 981- 1001
publication date 2015-08-01
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