Title :
A Method for Nonlinear Equation´s Simple Roots
Author_Institution :
Sci. Sch., Qingdao Technol. Univ., Qingdao, China
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;
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
DOI :
10.1109/CDEE.2010.9
