Three-step iterative methods with optimal eighth-order convergence

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Cordero, Alicia¹  Torregrosa, Juan R.¹  Vassileva, Maria P.² 

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Valencia 46022, Spain

[2] Inst Tecnol Santo Domingo INTEC, Santo Domingo, Dominican Rep

关键词: Nonlinear equations;    Iterative methods;    Convergence order;    Efficiency index;    Ostrowski's method;    Optimal order;   

DOI  :  10.1016/j.cam.2011.01.004

来源: Elsevier

【 摘 要 】

In this paper, based on Ostrowski's method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices are 1.682, which is optimal according to Kung and Traub's conjecture. Numerical comparisons are made to show the performance of the new family. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free