矩阵分裂序列与线性二级迭代法

MATRICES SPLITTING SEQUENCES AND TWO-STAGE ITERATIVE METHODS

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.