线性方程组的4种迭代方法

Four iterative methods to linear systems

研究了线性方程组的4种迭代方法——Jacobi迭代、Gauss-Seidel迭代、HSS迭代、Richardson迭代,给出了4种迭代方法收敛的充分条件。数值实验进一步表明,在大规模线性方程求解时,迭代矩阵谱半径的大小决定算法的收敛速度;在谱半径小于1的前提下,谱半径越小,则收敛速度越快。

Four iterative methods to linear systems,such as Jacobi,Gauss-Seidel,HSS,and Richardson iterative,are studied,and sufficient conditions for the convergence of these iterative methods are given.Numerical experiments further show that the size of spectral radius of iterative matrix determines convergence rate in solving large-scale linear systems. Under the premise of spectral radius of iterative matrix less than 1,the smaller the spectral radius,the faster convergence speed.