关于SSOR迭代法和Jacobi迭代法的敛散性

Convergence and Divergence of SSOR Iteration Method and Jacobi Method

本文证明了当Jacobi矩阵B非负时,解线性方程组(系数矩阵为不可约的SSOR法(0<ω<1)和Jacobi法同时敛散,给出了SSOR法迭代矩阵之谱半径ρ(φ)和ρ(B)之间的关系。

SSOR iterative method (0<ω<1) and Jacobi iterative method as the methods for solving system of linear equations with irredueiable matrix of coefficients are proved to be convergent and divergent simultaneously in case Jacobi maxtrix B is nonnegative. The rela- tion between the spectral radius ρ(φ_(?)) of SSOR iterative matrix and ρ(B) is given.