Article

convergence analysis of the global fom and gmres methods for solving matrix equations $axb=c$ with spd coefficients

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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