Improving the sor method

Abstract

In this paper we investigate how the convergence rate of the successive overrelaxation (SOR) method is affected if the linear system Ax = b is preconditioned by performing certain elementary row operations on A. It is shown that under some conditions the preconditioned SOR method gives improvement in the rate of convergence compared with the unpreconditioned SOR method for 0 < ω <1. Numerical examples are also given to show that the preconditioned SOR method gives tremendous improvement in the rate of convergence when the parameter ω>1.

Keywords:

• Linear systems
• iterative method
• successive overrelaxation (SOR) method
• preconditioned SOR method
• preconditioned linear system
• rate of convergence

C.R. Categories:

• G.1.3