SAOR Preconditioned Conjugate Gradient Method

For solving the large sparse symmetric and positive system of linear equations, the limitations of classical CG methods are now well known. So we exploit the preconditioned conjugate gradient (PCG) method. The key of this method is the construction of preconditioner. Consider SAOR iteration matrix method is not symmetric splitting, so we combine Alternating method with SAOR iteration method and present a class of preconditioned conjugate gradient method. The condition number for this method, which we refer to as SAOR-PCG, we develop a theoretical analysis that show that the better condition number is achieved. Furthermore, the Algorithm has been implemented and numerical results are included to illustrate the effectiveness of our approach.