An Analysis of a King-based Family of Optimal Eighth-order Methods
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Authors
Neta, Beny
Chun, Changbum
Subjects
iterative methods
order of convergence
basin of attraction
extraneous fixed points
weight functions
order of convergence
basin of attraction
extraneous fixed points
weight functions
Advisors
Date of Issue
2015
Date
2015
Publisher
Columbia International Publishing
Language
Abstract
In this paper we analyze an optimal eighth-order family of methods based on King's fourth order
method to solve a nonlinear equation. This family of methods was developed by Thukral
and Petković and uses a weight function. We analyze the family using the information on the
extraneous fixed points. Two measures of closeness of an extraneous points set to the imaginary
axis are considered and applied to the members of the family to find its best performer.
The results are compared to a modified version of Wang-Liu method.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.7726/ajac.2015.1001
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2005012)
Funder
Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2005012)
Format
17 p.
Citation
B. Neta, C. Chun, "An analysis of a King-based family of optimal eighth-order methods," American Journal of Algorithms and Computing, (2015) Vol. 2, No. 1, pp. 1-17
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.