关于Newton法的Kantorovich型定理及其优函数  

Concerning Kantorovich-type Theorem of Newton's Method and Its Majorants

作　　者：谢治州[1] 

机构地区：[1]黔南民族师范学院数学系,都匀贵州558000

出　　处：《数学进展》2012年第6期641-654,共14页Advances in Mathematics（China）

基　　金：贵州省科技厅自然科学基金项目(No.黔科合J字[201212310)

摘　　要：本文研究Newton法的Kantorovich型定理的特点及其对Newton法的半局部收敛性研究的思想方法,论述广义Lipschitz条件下的Kantorovich型定理的概括性和统一性.同时,在理论上当x_0取定时,针对每一个满足广义Lipschitz条件的光滑算子,给出优函数的一个构造方法.In this paper, the characteristics of Kantorovich-type theorem of Newton＇s method and the thoughtway on semilocal convergence properties of Newton＇s method are studied. The generality and the unity of Kantorovich-type theorem under the generalized Lipschitz condition are discussed. According to each smooth operator satisfying generalized Lipschitz condition when an initial guess x0 has been given, a construction method of the majorant is obtained theoretically.

关 键 词：NEWTON法 Kantorovich型定理 半局部收敛 优函数 广义Lipschitz条件 

分 类 号：O241[理学—计算数学]