EXTENDED ACCELERATED OVER RELAXATION (EAOR) METHOD FOR SOLUTION OF A LARGE AND SPARSE LINEAR SYSTEM

Abstract

In this research, we introduce a stationary iterative method called Extended Accelerated Over Relaxation (EAOR) method for solving linear systems. The method, an extension of the Accelerated Over Relaxation (AOR) method, was derived through the interpolation procedure with respect to the sub-matrices in application of a general linear stationary schemes. We studied the convergence properties of the method for special matrices such as 𝐿-, 𝐻-and irreducible diagonally dominant matrices and proposed some convergence theorems. Some numerical tests were carried out to test the efficiency of the proposed method with existing methods in terms of number of iterations, spectral radius and computational time. The results revealed the superiority of the proposed EAOR method over the AOR method in terms of convergence rate.