The accelerated over relaxation (AOR) method is the general method of Jacobi ,Gauss-Seidel, and successive over relaxation methods .It is used for solving systems of linear equations, but its rate of convergence is low. In this project we deal the refinement of accelerated over relaxation method which is the general method of Refinement of Jacobi, Refinement of Gauss-Seidel methods, and a numerical example is considered to show the efficiency or rate of convergence of the new method in comparison with other iteration methods. RAOR method needs only small number of iterations to find the approximate solution of system of linear equations when we compare with others.

A dissertation Submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics