Three-step iterative methods with eighth-order convergence for solving nonlinear equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:225

Article

Bi, Weihong¹  Ren, Hongmin²  Wu, Qingbiao¹ 

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Hangzhou Radio & TV Univ, Dept Elect & Informat, Hangzhou 310012, Zhejiang, Peoples R China

关键词: Nonlinear equations;    Iterative methods;    Newton's method;    King's methods;    Order of convergence;   

DOI  :  10.1016/j.cam.2008.07.004

来源: Elsevier

【 摘 要 】

A family of eighth-order iterative methods for the solution of nonlinear equations is presented. The new family of eighth-order methods is based on King's fourth-order methods and the family of sixth-order iteration methods developed by Chun et al. Per iteration the new methods require three evaluations Of the function and one evaluation of its first derivative. Therefore this family of methods has the efficiency index which equals 1.682. Kung and Traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2(n) (1). Thus we provide anew example which agrees with the conjecture of Kung-Traub for n = 4. Numerical comparisons are made to show the performance of the presented methods. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free