矩阵分裂序列与线性二级迭代法

doi:10.12286/jssx.2006.2.113

计算数学 ›› 2006, Vol. 28 ›› Issue (2): 113-120.DOI: 10.12286/jssx.2006.2.113

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矩阵分裂序列与线性二级迭代法

蔡放,熊岳山,

国防科技大学理学院数学系,国防科技大学计算机学院长沙 410073 长沙大学数学与信息科学系,长沙 410003,长沙 410073

出版日期:2006-02-14 发布日期:2006-02-14

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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.

MATRICES SPLITTING SEQUENCES AND TWO-STAGE ITERATIVE METHODS

Cai Fang (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) Xiong Yueshan (School of Computer, National University of Defense Technology, Changsha 410073, China)

Online:2006-02-14 Published:2006-02-14

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．

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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矩阵分裂序列与线性二级迭代法

MATRICES SPLITTING SEQUENCES AND TWO-STAGE ITERATIVE METHODS

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