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New class of eighth-order iterative zero-finders and their basins of attraction

Content Provider	Springer Nature Link
Author	Soleymani, Fazlollah
Copyright Year	2012
Abstract	A three-step class of iterative methods without memory for approximating the simple roots of single valued nonlinear equations is suggested. Theoretical proof shows that it has eighth-order convergence by consuming three evaluations of the function and one of its first order derivative per full iteration. One method of the class is generalized for finding the multiple zeros when the multiplicity of the roots are not known. The analytical results are supported through numerical works to put on show the efficacy of the new methods. Moreover, the basins of attraction for some of the high order methods in the complex plane will be given.
Starting Page	67
Ending Page	79
Page Count	13
File Format	PDF
ISSN	10129405
Journal	Afrika Matematika
Volume Number	25
Issue Number	1
e-ISSN	21907668
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2012-08-25
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multi-point methods Optimal efficiency index Basin of attraction Fractal Rate of convergence, degree of approximation Strange attractors, chaotic dynamics Fractals Polynomials; rational maps; entire and meromorphic functions Mathematics Applications of Mathematics History of Mathematical Sciences Mathematics Education
Content Type	Text
Resource Type	Article
Subject	Mathematics

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