Parallelization of Iterative Method

用迭代法对线性方程组进行了数值计算，提出了一种新的预处理迭代法，并通过数值实验证明了该方法比SOR法更快。我们的方法是高斯-赛德尔方法的预处理矩阵的一个积极的参数。我们还推导了我们所提出的方法的收敛性定理。并给出了预条件矩阵最优参数的估计公式。通过对对流扩散问题的数值计算，证明了本文方法的有效性。众所周知，当系数矩阵A具有H矩阵时，迭代法可以用于求解线性方程组。因此，我们提出了一种简单的判断H-矩阵的先验方法，并指出这种预条件迭代方法对于提高求解各种科学和工程领域中的线性方程组的性能是有效的。

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.