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.
