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Proceedings of 2009 International Workshop on Information Security and Application (IWISA 2009)

Qingdao, China, November 21-22, 2009

Editors: Feng Gao and Xijun Zhu

AP Catalog Number: AP-PROC-CS-09CN004

ISBN: 978-952-5726-06-0

Page(s): 588-590

A Mean Newton's Method for Simple Roots

Chunmei Chi

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In this work, we study the convergence behavior of a modified Newton's method based on Simpson integral rule. The convergence properties of this method for solving equations which have simple roots have been discussed and it has been shown that it converges cubically to simple roots. And the values of the corresponding asymptotic error constants of convergence are determined. Theoretical results have been verified on the relevant numerical problems. A comparison of the efficiency of this method with other mean-based Newton's methods, based on the arithmetic, harmonic means and geometric means, is also included.

Index Terms

Newton's method, mean-based method, order of convergence, asymptotic error constant, Simpson integral rule

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