Extrapolated refinement of generalized gauss- seidel scheme For solving systems of linear equations

Abstract

In this thesis, Extrapolated Refinement of Generalized Gauss-Seidel scheme for solving system of linear equations has been developed. In order to accelerate the rate of convergence of the scheme, the one-parameter family of splitting procedure has been introduced in order to attain the largest rate of convergence. To validate the proposed method, two 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. Finally, the results showed that the Extrapolated Refinement of Generalized Gauss-Seidel scheme is more efficient than the other three schemes considered.