简化Newton法的点估计(为庆贺游兆永教授60寿辰而作)  

Point Estimates for Simple newton's Method

作　　者：张讲社[1] 

机构地区：[1]西安交通大学

出　　处：《工程数学学报》1991年第2期169-174,共6页Chinese Journal of Engineering Mathematics

摘　　要：本文通过对强函数的分析将Smale在1986年数学大会上报告的关于Newton迭代点估计的工作推广到简化Newton法,证明了当α(z,f)≤1/13时,对于所有实的或复的Banach空间E到,型空间F的解析映射f和z∈E,z是f的一个逼近零点.而当时z是f的一个第二类逼近零点.In this paper we generalize the Smale's work on point estimates for newton's method, which is reported on international Congress of Mathematicians, to simple Newton's method through analyses merit function. We have proved that for any analytic map f from one bonach space E (real or complex) to thesame type space F and any z∈E, if α(z, f)≤1/13,then z is a approximate zero point, and if a(z, f)≤9-61/16; then z is a second class approximate zero point off.

关 键 词：NEWTON法 点估计 B空间 解析映射 

分 类 号：O241.7[理学—计算数学]