关于M矩阵的线性系统一个新的AOR预处理方法(英文)  

A New Preconditioned AOR Iterative Method for Linear System with M-Matrices

作　　者：谈雪媛[1] 

机构地区：[1]南京师范大学数学科学学院,江苏省大规模系统数值模拟重点实验室,南京210023

出　　处：《南京师大学报（自然科学版）》2014年第4期7-13,共7页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of China(2010101GZ30005);Jiangsu Innovation Fund for Doctor of Science(CX07B-027z)

摘　　要：本文研究M矩阵的预处理AOR方法,并给出新的预处理子I+Sα+SM+Sδ.新的预处理子是基于系数矩阵A的上三角部分绝对值最大元素,次对角元素以及最后一列元素构建.我们证明此法将加速AOR迭代速率,并通过与其他三个预处理子的比较说明新的预处理子更有效.数值例子验证了此预处理方法的有效性.The purpose of this paper is to investigate the preconditioned AOR method with a new preconditioner denoted as I＋Sα＋SM＋Sδ for M-matrix. The new preconditioner is constructed by considering the largest absolute value of the upper triangular part,the secondary diagonal and the last column of the coefficient matrix A. We prove that the rate of the AOR iterative method can be accelerated,and give the comparison with other three preconditioners to show the new pre-conditioner is more effective. Numerical example demonstrates the effectiveness of this preconditioning scheme.

关 键 词：线性系统 AOR迭代方法 预处理子 M-矩阵 

分 类 号：O241.6[理学—计算数学]