在二层迭代情况下AOR方法和SOR方法收敛性的比较(英文)  

THE CONVERGENCE COMPARISON OF THE AOR AND SOR METHODS USED IN TWO-STAGE ITERATIVE METHODS

作　　者：滑伟[1] 吴业军[2] 

机构地区：[1]南京工程学院基础部,南京210013 [2]南京大学数学系,南京210093

出　　处：《南京大学学报（数学半年刊）》2008年第1期56-66,共11页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by the Natural Science Foundation of Nanjing Institute of Technology under grants KXJ06051.

摘　　要：在不同情况下AOR和SOR方法有各自的优点,本文通过利用当一个线性系统的系数矩阵为(1,1)相容次序矩阵且它的Jacobi矩阵的特征值均为纯虚数或0时AOR迭代方法收敛的最佳参数以及它的最佳谱半径与SOR方法的比较,研究了在二级迭代的情况下这两种方法该如何选取.When the coefficient matrix of a linear system is(1,1)consistently ordered matrix and the eigenvalues of its Jacobi matrix are all pure imaginaries or zeroes,the convergence and the optimum parameters of its AOR iterative method and a comparison between its optimum spectral radius and that of SOR method are shown.Since the AOR and SOR methods have their own advantages respectively under different conditions,how to choose one of them for the convergence of the two-stage iterative methods for the solution of linear system is studied.

关 键 词：二级迭代 相容次序矩阵 AOR方法 SOR方法 最佳参数 谱半径 

分 类 号：O241.6[理学—计算数学]