求解Hilbert矩阵线性方程组的SOR迭代预处理方法

SOR Preprocessing Method for Hilbert Matrix Linear Equations

选择了求解Hilbert矩阵线性方程组的三种数值解方法,提出了SOR迭代中的松弛因子的预处理方法,比较了高斯-赛德尔迭代和SOR迭代数值解的迭代收敛次数,并给出了SOR迭代收敛最快时的松弛因子取值.最后通过SOR迭代解分量及误差范围,说明了提出的SOR迭代预处理方法是有效的.

In this paper,we select three numerical methods for solving Hilbert matrix linear equations,propose a relaxation factor preprocessing method of the SOR iteration,compare Gauss-Seidel method with SOR method by their numbers of iterations needed for convergence,and note the best relaxation factor for the fastest SOR iterative convergence.With the solution components and the error range of SOR iterative numerical solution,we perceive the effectiveness of the preprocessing method of SOR iteration.