Successive Over Relaxation Method Which Uses Matrix Norms for Newton Operator

Abstract

Succesive Overrelaxation method (S.O.R.) is a well known iterative method which is very sensitive to extensions and modifications as an attempt to obtaining other iterative methods. An algorithm for S.O.R functional iteration which uses matrix norms for the Jacobi iteration matrices rather than the usual Power method, feasible in Newton Operator for the solution of nonlinear system of equations is proposed. We modified the S.O.R. iterative method known as Multiphase S.O.R. method for Newton operator. Numerical example is given and results from our method are compared with an existing classical S. O.R method. It is shown that our method has superiority over the classical S.O.R. method.

Keywords : Gauss- Siedel method, S.O.R method, Newton method, matrix norm.