AOR与USSOR迭代法的比较  

Comparison Between USSOR and AOR Iterative Methods

作　　者：李荣[1,2] 

机构地区：[1]陕西师范大学,陕西西安710062 [2]运城学院师范分院,山西运城044000

出　　处：《忻州师范学院学报》2012年第2期28-30,共3页Journal of Xinzhou Teachers University

基　　金：国家自然科学基金资助项目(10071048)

摘　　要：AOR(快速超松弛法)和USSOR(非对称逐次超松弛法)的迭代矩阵中都含有两参数,且这两种迭代更具广泛性。文章首先论证了当ω1=γ,ω2=ω,且0≤γ≤ω≤1(ω≠0)时,USSOR迭代优于AOR迭代;其次证明了预条件矩阵Pm下这种结论也成立。由于USSOR法的迭代矩阵形式较复杂,计算麻烦,要直接判别其敛散性是比较困难的,因此可通过AOR迭代矩阵的谱半径来判断USSOR迭代的敛散性,这样就简单多了。最后通过两个数值例子进行验证。Both USSOR and AOR methods are widely used owning to their iterative matrix containing two parameters. This paper proves the iterative methods USSOR superior to AOR under the condition ω1=γ,ω2=ω,to, and 0≤γ≤ω≤1（ω≠0）. This is true of the precon- dition matrixPm. Besides, because it is difficult to identify the convergence of USSOR iterative due to its complicated matrix to be figured out, this paper proposes a much convenient way using the spectral radius of AOR iterative matrix to solve this problem. Two examples are given to verify this method.

关 键 词：USSOR迭代 谱半径 敛散性 AOR迭代 

分 类 号：O246[理学—计算数学]