Self-Adaptive Extrapolated Gauss-Seidel Iterative Methods

Abstract

In this paper, we consider a self-adaptive extrapolated Gauss-Seidel method for solving the Hermitian positive definite linear systems. Based on optimization models, self-adaptive optimal factor is given. Moreover, we prove the convergence of the self-adaptive extrapolated Gauss-Seidel method without any constraints on optimal factor. Finally, the numerical examples show that the self-adaptive extrapolated Gauss-Seidel method is effective and practical in iteration number.