Wolfram Library Archive


Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings
Title

Sixth-order modifications of Newton’s method based on Stolarsky and Gini means
Authors

Djordje Herceg
Organization: Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad
Dragoslav Herceg
Organization: Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad
Journal / Anthology

Journal of Computational and Applied Mathematics
Year: 2014
Volume: 267
Page range: 244–253
Description

In this article we present sixth order methods developed by extending third order methods of Herceg and Herceg (2013) for solving nonlinear equations. The methods require only four function evaluations per iteration. In this regard the efficiency index of our methods is 61/4 ≈ 1.56508. Considered methods are based on Stolarsky and Gini means and depend on two parameters. Sixth order convergence of considered methods is proved, and corresponding asymptotic error constants are expressed in terms of two parameters. Numerical examples, obtained using Mathematica with high precision arithmetic, are included to demonstrate convergence and efficacy of our methods. For some combinations of parameter values, the new sixth order methods produce very good results on tested examples, compared to the results produced by some of the sixth order methods existing in the related literature.
Subject

*Applied Mathematics
Keywords

Nonlinear equations, Newton’s method, Sixth order methods, Gini mean, Stolarsky mean


Translate this page: