Publication:
A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points

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Authors
Neta, Beny
Geum, Young Hee
Kim, Young Ik
Subjects
Multiple-zero finder
Extraneous fixed point
Modified Newton’s method
Basins of attraction
Advisors
Date of Issue
2016
Date
2016
Publisher
Elsevier Inc.
Language
Abstract
A class of three-point sixth-order multiple-root finders and the dynamics behind their extraneous fixed points are investigated by extending modified Newton-like methods with the introduction of the multivariate weight functions in the intermediate steps. The multivariate weight functions dependent on function-to-function ratios play a key role in constructing higher-order iterative methods. Extensive investigation of extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction. Numerical experiments applied to a number of test equations strongly support the underlying theory pursued in this paper. Relevant dynamics of the proposed methods is well presented with a variety of illustrative basins of attraction applied to various test polynomials.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1016/j.amc.2016.02.029
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 funded by the Ministry of Education under the research grant (Project Number: 2015-R1D1A3A-01020808)
Funder
Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education under the research grant (Project Number: 2015-R1D1A3A-01020808)
Format
21 p.
Citation
Applied Mathematics and Computation 283 (2016) 120–140
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.
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