Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems

被引：66

作者：

Hueso, Jose L. ^{[1
]}

Martinez, Eulalia ^{[2
]}

Teruel, Caries ^{[1
]}

机构：

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

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 275卷

关键词：

Nonlinear systems; Iterative methods; Convergence order; Computational cost; Efficiency; Dynamics; QUADRATURE-FORMULAS; NEWTONS METHOD; EQUATIONS; CONSTRUCTION;

D O I：

10.1016/j.cam.2014.06.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we present a new family of iterative methods for solving nonlinear systems that are optimal in the sense of Kung and Traub's conjecture for the unidimensional case. We generalize this family by performing a new step in the iterative method, getting a new family with order of convergence six. We study the efficiency of these families for the multidimensional case by introducing a new term in the computational cost defined by Grau-Sanchez et al. A comparison with already known methods is done by studying the dynamics of these methods in an example system. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：412 / 420

页数：9

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