A Method for Nonlinear Equation´s Simple Roots

Author

Gao, Feng

Author_Institution

Sci. Sch., Qingdao Technol. Univ., Qingdao, China

fYear

2010

fDate

23-24 Oct. 2010

Firstpage

3

Lastpage

5

Abstract

In this paper, we present 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. The values of the corresponding asymptotic error constants of convergence are determined. Theoretical results have been verified on the relevant numerical problems. In addition, we also point out that if combined with other numerical methods such as improved Ostrowski´s method, the SN method can be more efficient.

Keywords

Newton method; convergence of numerical methods; integral equations; nonlinear equations; Simpson integral rule; asymptotic error constants; convergence behavior; modified Newton method; nonlinear equation simple root; numerical method; Acceleration; Approximation methods; Convergence; Newton method; Nonlinear equations; Tin; Newton´s method; Simpson integral rule; convergence;

fLanguage

English

Publisher

ieee

Conference_Titel

Cryptography and Network Security, Data Mining and Knowledge Discovery, E-Commerce & Its Applications and Embedded Systems (CDEE), 2010 First ACIS International Symposium on

Conference_Location

Qinhuangdao

Print_ISBN

978-1-4244-9595-5

Type

conf

DOI

10.1109/CDEE.2010.9

Filename

5759407