最佳双松弛因子迭代法的存在条件  

On Conditions of Iteration Method with Two Optimal Relaxation Factors

作　　者：唐永建[1] 向隆万[2] 

机构地区：[1]上海电力学院基础部,上海200090 [2]上海交通大学应用数学系,上海200030

出　　处：《上海电力学院学报》2001年第1期15-19,共5页Journal of Shanghai University of Electric Power

摘　　要：对于大型线性代数方程组AX = b,通常采用单松弛因子进行超松弛迭代. 作者在进行汽轮发电机氢内冷转子三维温度场的计算中,发现采用双松弛因子迭代比单松弛因子迭代速度更快. 在深入研究的基础上,本文证明了在某种条件下,当A为时,双松弛因子迭代矩阵的谱半径小于单松弛因子迭代矩阵的谱半径. 算例表明这种迭代格式的有效性.For a large scale linear equations AX = b, if A has form as ,this paper proves that using two relaxation factors would be better than conventional SOR iteration with single relaxation factor under some conditions. Some examples show the effectiveness of the scheme. The authors used two relaxation factors to calculate the 3D steady temperature distribution in a hydrogen inner-cooled turbogenerator rotor and got very good results.

关 键 词：线性代数方程组 松弛因子 迭代法 谱半径 

分 类 号：O241.6[理学—计算数学] O242.26[理学—数学]