| AOR与USSOR迭代法的比较 |
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| 引用本文： | 李荣.AOR与USSOR迭代法的比较[J].忻州师范学院学报,2012,28(2):28-30. |
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| 作者姓名： | 李荣 |
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| 作者单位： | 陕西师范大学,陕西西安710062 运城学院师范分院,山西运城044000 |
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| 基金项目： | 国家自然科学基金资助项目(10071048) |
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| 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。
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| 关 键 词： | USSOR迭代 谱半径 敛散性 AOR迭代 |
Comparison Between USSOR and AOR Iterative Methods |
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| LI Rong.Comparison Between USSOR and AOR Iterative Methods[J].Journal of Xinzhou Teachers University,2012,28(2):28-30. |
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| Authors: | LI Rong |
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| Institution: | LI Rong1,2(1.Shannxi Normal University,Xi’an 710062,China; 2.Normal Branch Yuncheng University,Yuncheng 044000,China) |
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| Abstract: | 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,and 0≤γ≤ω≤1(ω≠0).This is true of the precondition 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. |
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| Keywords: | USSOR iterative methods spectral radius convergence AOR iterative methods |
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