Modified SAOR Preconditioned Conjugate Gradient Method

This paper is investigated a preconditioned conjugate gradient method in solving a large linear algebraic system. 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 2,1 propose a mew type of preconditioned conjugate gradient method, which is called modified SAOR PCG in brief. The preconditioned M is derived on the base of SAOR. 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 modified SAOR PCG method is better than the classical iterative method(such as Gauss-Seidel,SOR) and the traditional CG method as well as SSOR PCG...