FBTOR方法及其收敛性

Forward and Backward Tor Method and Its Convergence

本文构造出一种迭代求解线性方程组的向前向后 TOR 方法——FBTOR 方法,它包含了熟知的 Jacobi,Gauss—Seidel、SOR、AOR、SAOR 及FBAOR 方法,并讨论了系数阵为对称正定律、不可约 H—阵、正定阵、广义正定阵及稳定阵时 FBTOR 方法的收敛性。

In this paper,we construct a kind of forward and backward TOR method for iterative solution of linear systems——FBTOR method,it includes the well—known Jacobi method,Gauss—seidel method,SOR method,AOR method,SAOR method and FBAOR method.This paper chi- efly discusses the convergence of FBTOR method in the cases where the coefficient matrices are symmetric positively definite matrites,irreducible H—matrices,positively definite matrites,generalized positively definite matrices and stable matrices respectively.