求解大型线性方程组的一类非定常内外迭代法

1 引 言 求解大型线性方程组 Ax=b, A∈R~(?),det(A)≠0. x,b∈R~n (1.1)的内外迭代法,首先由Nichols于1973年提出。由于这类算法在求解大型问题。特别对由边值问题离散化得到的大型稀疏方程组求解,显示了优越性,而受到众多的关注。1991年,Lanzkron.Rose.Szvld等人进一步降其发展成为成套迭代法,为预条件组的近似及同步和

THE NON-STATIONARY INNER/OUTER ITERATIVE METHOD FOR THE SOLUTION OF LARGE LINEAR SYSTEMS

In this paper, a family of special non-stationary inner/outer iterative methods is presented for solving large linear systems of equations. Combining a splitting of matrix with a update algorithm is the basic idea of the method. We have showed that if the outer splitting is convergent then. for a suitable initial matrix which is required by the update algorithm .the inner/outer method is convergent for any number of inner iteration. We also analyse block form of the methods. The numberical tests show that the method is successful.