AOR迭代法的收敛性

1.引言 1]定义了解线性方程组A_x=b的AOR迭代法,它以SOR迭代为特例,而且适当选取参数,有可能比SOR方法收敛快(见2]).众所周知,使 AOR方法有意义的最基本条件是A的对角元素都不为零.然而,在实际计算中,有时需要求解的线性方程组其系数矩阵存在零对角元素.例如3]中研究的线性方程组的系数矩阵具有如下形式:

CONVERGENCE OF THE AOR ITERATIVE METHOD

In this paper, we define the generalized AOR method and give a theorem of Stein-Rosenberg type on the AOR method. We investigate the monotone convergence boundof the AOR method, and consider the special case where the coefficient matrix is an M-matrix. A convergence theorem is given whenever the coefficient matrix is an H-matrix.