Local Convergence of an Optimal Eighth Order Method under Weak Conditions

Algorithms

Ioannis K. Argyros¹  Ramandeep Behl²  S.S. Motsa² 

[1] Cameron University, Department of Mathematics Sciences Lawton, OK 73505, USA; E-Mail:;School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa; E-Mail:

关键词: Newton-like method;    local convergence;    efficiency index;    optimum method;   

DOI  :  10.3390/a8030645

来源: mdpi

【 摘 要 】

We study the local convergence of an eighth order Newton-like method to approximate a locally-unique solution of a nonlinear equation. Earlier studies, such as Chen et al. (2015) show convergence under hypotheses on the seventh derivative or even higher, although only the first derivative and the divided difference appear in these methods. The convergence in this study is shown under hypotheses only on the first derivative. Hence, the applicability of the method is expanded. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies cannot apply.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.