预处理后新分裂下的SOR迭代法收敛性讨论

The convergence discussion of the SOR iterative method in preconditioned for the new splitting

在求解大型线性方程组Ax=b时,常采用预处理方法求解,也就是对方程组两边同时乘以非奇异矩阵P再求解.运用矩阵分裂理论及比较定理,给出一种预处理后改进的SOR迭代方法,与现有的方法进行比较,证明这种方法不仅能加速SOR迭代法的收敛性,而且优于一般的预处理方法.最后给出一个数值例子.

When solving the large linear systems Ax=b,the preconditioned method was used generally,it was let nonsingular matrix P to mount the linear systems.This paper by using matrix iterative analysis and comparison theorems,made an improved SOR iterative method in preconditioned,then proved the improved method not only to accelerate the SOR iterative method,but also to excelled the general preconditioned SOR method.Last the numerical example was given.