An optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed points
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Authors
Rhee, Min Surp
Kim, Young Ik
Neta, Beny
Subjects
Eighth-order convergence
Weight function
Asymptotic error constant
Efficiency index
Purely imagninary extraneous fixed point
Basin of attraction
Weight function
Asymptotic error constant
Efficiency index
Purely imagninary extraneous fixed point
Basin of attraction
Advisors
Date of Issue
2018
Date
Publisher
Taylor & Francis
Language
Abstract
In this paper, we not only develop an optimal class of three-step eighth-order methods with higher order weight functions employed in the second and third sub-steps, but also investigate their dynamics underlying the purely imaginary extraneous fixed points. Their theoretical and computational
properties are fully described along with a main theorem stating the order of convergence and the asymptotic error constant as well as extensive studies of special cases with rational weight functions. A number of numerical examples are illustrated to confirm the underlying theoretical development. Besides, to show the convergence behaviour of global character, fully explored is the dynamics of the proposed family of eighth-order methods as well as an existing competitive method with the help of
illustrative basins of attraction.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1080/00207160.2017.1367387
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
38 p.
Citation
M.S. Rhee, Y.I. Kim, B. Neta, "An optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed points," International Journal of Computer Mathematics, (2017), 38 p.
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.