偏序下的区间松弛法

§1. 引言 本文给出了求解非线性方程组 f(x)=0,f:D?R~n→R~m (1.1)在偏序下的区间松弛法,它是在1]的基础上将区间迭代与Newton-SOR 迭代结合得到的一种便于计算且收敛较快的序区间N-SOR松弛法,也是单调N-SOR迭代法的推广.§2给出了偏序下的区间Krawczyk算子,它是区间 Newton算子的推广,同样具

INTERVAL RELAXATION METHODS UNDER PARTIAL ORDERING

The order interval krawczyk type operator K_Ω(X) and order interval Newton-SOR relaxa-tion methods for solution of nonlinear equations are construced. The methods are based on or-der interval Newton operator N_Ω(X) combined with the Newton-SOR methods. This paperproves that K_Ω.(X)?N_Ω(X), and that the iterative sequence {x~((i))} obtained by the newmethods converges faster to the solution of nonlinear equations than the interval Newton itera-tive sequence. Some numerical examples for solving nonlinear difference equations are given.