An Intelligent Method for Accelerating the Convergence of Different Versions of SGMRES Algorithm

Abstract

In a wide range of applications, solving the linear system of equations Ax = b is appeared. One of the best methods to solve the large sparse asymmetric linear systems is the simplified generalized minimal residual (SGMRES(m)) method. Also, some improved versions of SGMRES(m) exist: SGMRES-E(m, k) and SGMRES-DR(m, k). In this paper, an intelligent heuristic method for accelerating the convergence of three methods SGMRES(m), SGMRES-E(m, k), and SGMRES-DR(m, k) is proposed. The numerical results obtained from implementation of the proposed approach on several University of Florida standard matrixes confirm the efficiency of the proposed method.