A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem

被引：16

作者：

Andreu, Carlos ^{[1
]}

Cambil, Noelia ^{[1
]}

Cordero, Alicia ^{[1
]}

Torregrosa, Juan R. ^{[1
]}

机构：

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

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 232卷

关键词：

Nonlinear equation; Iterative method; Derivative-free scheme; Order of convergence; Basin of attraction; Efficiency index; NONLINEAR EQUATIONS; EFFICIENT;

D O I：

10.1016/j.amc.2014.01.056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A derivative-free optimal eighth-order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences. Its performance, along with several other derivative-free methods, is studied on the specific problem of Danchick's reformulation of Gauss' method of preliminary orbit determination. Numerical experiments show that such derivative-free, high-order methods offer significant advantages over both, the classical and Danchick's Newton approach. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：237 / 246

页数：10

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