基于最小二乘法的SOR法松弛因子自动生成算法  

The Automatic Generation of Relaxation Factor in SOR Method Based on Least Square Method

作　　者：杨继业[1] 李雨青[1] 

机构地区：[1]宁夏大学数学与计算机学院,银川750021

出　　处：《赣南师范学院学报》2008年第3期34-37,共4页Journal of Gannan Teachers' College(Social Science(2))

摘　　要：基于使每一迭代步线性方程组中各个方程的余量平方和最小的原理,给出了松弛因子的自动生成方法,从而有效地避免了最佳松弛因子的选取带来的不便.并通过数值实验说明此算法切实可行,只要系数矩阵满足严格对角占优或弱对角占优且不可约条件就能够取得很好的收敛效果.In this paper a new method is presented to generate the relaxation factor automatically by minimizing the squared sum- mation of the residual of each equation in linear system with no fatigue work on the relaxation factor any more. And some numerical experiments are carried out as well. The result indicates that the algorithm developed in this paper is feasible and of desirable convergence efficient if the coefficient matrix is strictly diagonally dominant or weakly diagonally dominant and irreducible.

关 键 词：迭代法 超松弛 松弛因子 

分 类 号：O241.6[理学—计算数学]