Optimal Newton-Secant like methods without memory for solving nonlinear equations with its dynamics

被引：17

作者：

Salimi, Mehdi ^{[1
]}

Lotfi, Taher ^{[2
]}

Sharifi, Somayeh ^{[3
]}

Siegmund, Stefan ^{[1
]}

机构：

[1] Tech Univ Dresden, Dept Math, Ctr Dynam, D-01062 Dresden, Germany

[2] Islamic Azad Univ, Hamedan Branch, Dept Math, Hamadan, Iran

[3] Islamic Azad Univ, Hamedan Branch, Young Researchers & Elite Club, Hamadan, Iran

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2017年 / 94卷 / 09期

关键词：

Multi-point iterative methods; Newton-Secant method; Kung and Traub's conjecture; 65H04; 65H05; ITERATIVE METHODS; MULTIPOINT METHODS; 3-POINT METHODS; OPTIMAL ORDER; CONVERGENCE; FAMILY;

D O I：

10.1080/00207160.2016.1227800

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct two optimal Newton-Secant like iterative methods for solving nonlinear equations. The proposed classes have convergence order four and eight and cost only three and four function evaluations per iteration, respectively. These methods support the Kung and Traub conjecture and possess a high computational efficiency. The new methods are illustrated by numerical experiments and a comparison with some existing optimal methods. We conclude with an investigation of the basins of attraction of the solutions in the complex plane.

引用

页码：1759 / 1777

页数：19

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