| 矩阵分裂序列与线性二级迭代法 |
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| 引用本文： | 蔡放,熊岳山.矩阵分裂序列与线性二级迭代法[J].计算数学,2006,28(2):113-120. |
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| 作者姓名： | 蔡放 熊岳山 |
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| 作者单位： | 1. 国防科技大学理学院数学系,长沙,410073;长沙大学数学与信息科学系,长沙,410003
2. 国防科技大学计算机学院,长沙,410073 |
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| 基金项目： | 浙江省湖州市自然科学基金 |
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| 摘 要： | 本文讨论线性非定常二级迭代法的收敛性．对于一般的基于矩阵分裂序列的迭代法,针对分裂序列本身找到了一种新的且相对较弱的收敛性条件,并因此得到了由非定常二级迭代法推广而来的广义二级迭代法的收敛结果．从而,用一种新的方法证明了非定常二级迭代法的收敛性．
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| 关 键 词： | 线性方程组 二级迭代法 矩阵分裂 |
| 收稿时间： | 2003-11-02 |
| 修稿时间： | 2003-11-022005-04-14 |
MATRICES SPLITTING SEQUENCES AND TWO-STAGE ITERATIVE METHODS |
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| Cai Fang,Xiong Yueshan.MATRICES SPLITTING SEQUENCES AND TWO-STAGE ITERATIVE METHODS[J].Mathematica Numerica Sinica,2006,28(2):113-120. |
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| Authors: | Cai Fang Xiong Yueshan |
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| Institution: | Department of Mathematics, School of Science, National University of Defense Technology, Changsha 410073, China; Department of Mathematics and Information Science, ChangSha University, Changsha 410003, China; School of Computer, National University of Defense Technology, Changsha 410073, China |
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| Abstract: | This paper discusses the convergence of the non-stationary two-stage iterative methods for linear systems. A sort of new and weak convergent condition satisfied by the matrices splitting sequences is found for the iterative methods with the matrices splitting sequences. We then obtain the convergent result of the generalized two-stage iterative methods, which are the generalization of the non-stationary two-stage iterative methods. Consequently, the convergence of the non-stationary two-stage iterative methods is proofed over again through a new approach. |
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| Keywords: | Linear systems Two-stage iterative methods Matrices splitting |
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