Parallelization of Iterative Method

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The numerical computation was carried out to solve the linear system by using the iterative method.In this project we presented the new preconditioning iterative method and showed that our method is faster than SOR method with some numerical experiments. Our method is the Gauss-Seidel Method for the preconditioning matrix with a positive parameter. We also derived convergence theorem of our proposed method. Moreover, we obtained the estimation formula of optimum parameter for the preconditioned matrix. Further we tested the effectivity of the proposed method and convective diffusion problem, and we obtained that our method is effective in solving such a practical problem.It is well known that if coefficient matrix A has H-matrix, then the iterative method is able to use solving the linear systems. Thus, we developed simple a priori method for judging H-matrix.It has been pointed out that our preconditioning iterative method is effective to improve the performance to solve the linear system in various fields of science and engineering.