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

作　　者：刘瑞华 邹洋杨 谢挺 LIU Ruihua;ZOU Yangyang;XIE Ting(Liangjiang Artificial Intelligence College,Chongqing University of Technology,Chongqing 400054,China;School of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学,两江人工智能学院,重庆400054 [2]重庆理工大学,理学院,重庆400054

出　　处：《高等数学研究》2020年第1期60-63,共4页Studies in College Mathematics

基　　金：重庆市自然科学基金面上项目(cstc2019jcyj-msxmX0500);重庆理工大学校级项目(2016YB30)

摘　　要：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.

关 键 词：SOR迭代法 预处理方法 希尔伯特矩阵 松弛因子 

分 类 号：O241.6[理学—计算数学]