HOMOCENTRIC CONVERGENCE BALL OF THE SECANT METHOD

作     者：Liang Kewei 

作者机构：Dept. of Math. Zhejiang Univ. Hangzhou 310027 China 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2007年第22卷第3期

页      面：353-365页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：secant method semi-local convergence theorem local convergence theorem convergence ball,homocentric ball. 

摘      要：A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper. For every convergence theorem, a convergence ball is respectively introduced, where the hypothesis conditions of the corresponding theorem can be satisfied. Since all of these convergence balls have the same center x^＊, they can be viewed as a homocentric ball. Convergence theorems are sorted by the different sizes of various radii of this homocentric ball, and the sorted sequence represents the degree of weakness on the conditions of convergence theorems.