Extrapolated refinement of generalized gauss- seidel scheme for solving system of linear equations

Abstract

In this paper, Extrapolated Refinement of Generalized Gauss-Seidel scheme for solving system of linear equations has been presented. In order to accelerate the rate of convergence of the scheme, the one-parameter family of splitting procedure has been introduced and the convergence of the method is well established. To validate the proposed method, three numerical examples were considered. Comparisons were made among Refinement of Generalized Jacobi, Generalized Gauss-Seidel, Refinement of Generalized Gauss-Seidel and Extrapolated Refinement of Generalized Gauss-Seidel schemes with respect to the number of iterations to converge, computational running time and storage capacity. The numerical results presented in tables show that the Extrapolated Refinement of Generalized Gauss-Seidel scheme is more efficient than the other three schemes considered for comparison.