Preconditioned modified AOR method for systems of linear equations

In this paper, we present three kinds of preconditioners for preconditioned modified accelerated over-relaxation (PMAOR) method to solve systems of linear equations. We show that the spectral radius of iteration matrix for the PMAOR method is smaller than that for modified accelerated over-relaxation (MAOR) method including their comparison. The comparison results show that the convergence rate of the PMAOR method is better than the rate of the MAOR method. We provide some numerical results for the evidence of our method. Also we compare our numerical results with solutions by variational iteration method. Copyright (C) 2009 John Wiley & Sons, Ltd.