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.
出处
《南京大学学报（数学半年刊）》
CAS
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.
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
two-stage iterative methods
consistently ordered matrix
AOR method
SOR method
the optimum parameter
spectral radius
