SAOR-AL Preconditioned Conjugate Gradient Method

This paper is investigated a preconditioned conjugate gradient method in solving a linear algebraic system of large sparse symmetric and positive equations. There are four chapters in this paper altogether.In chapter 1, the overview is given about the study at present in the world.In chapter 2. I propose a new type of preconditioned conjugate gradient method, which is called SAOR-AL-PCG in brief. The preconditioner M is derived on the base of SAOR and the alternating method .Then we use conjugate gradient method to solve the preconditioned system MAx = Mb.In chapter 3, I analyze this algorithm and draw a conclusion its condition number is lower than CG algorithm's.In chapter 4,some examples are given to illustrate that the convergence of SAOR-AL-PCG method is better than the classical iterative method(such as Jacobi. Gauss ?Seidel. SOR) and the traditional CG method as well as SSOR-PCG.