SOR迭代法收敛性的判定

CRITERIA OF CONVERGENCE OF SOR ITERATIVE METHOD

本文在[1～3]基础上,给出 SOR 迭代法更一般适用的收敛充分条件,并得到了误差估计式,对ω=1情况,改进了[1]的主要结果。

In this paper,we modified the main results of [1].we give several more general criteria of Convergence of SOR method. We assume that the Jacobi iterative matrix is given by B′=(b_(ij)~′) and () We proved: (1)(). then the SOR method converges. (2) If ω=1,(), then the Gauss-seidel mothod converges. (3)If ω=ω_0,(), then the SOR method converges. (4)If ω=1,(), then the Gauss-seidel method converg()s.