To the question of efficiency of iterative methods

详细信息    查看全文

• 作者：Tamara Kogan^a ; Luba Sapir^b ; ^{lsapir@bgu.ac.il} ; Amir Sapir^c ; ^d ; ^{amirsa@cs.bgu.ac.il} ; Ariel Sapir^e ; ^{arielsa@cs.bgu.ac.il}
• 关键词：Iterative methods ; One-point method without memory ; Efficiency index ; Informational efficiency ; Computational efficiency ; Order of convergence
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：66
• 期：Complete
• 页码：40-46
• 全文大小：727 K
• 卷排序：66

文摘

In this paper we prove that, among all one-point iterative processes without memory of order pp, the most efficient processes are of order p=3p=3. Moreover, the computational efficiency of one-point iterative processes without memory decreases to 11 as pp increases, i.e., the efficiency index of higher order of convergence methods is low. We find the upper and lower bounds of the Ostrowski–Traub index of computational efficiency in a wider class of iterative methods with unit informational efficiency.