Convergence regions for the Chebyshev--Halley family
Campos, Beatriz (Institut Universitari de Matemàtiques i Aplicacions de Castelló)
Canela Sánchez, Jordi (Institut Universitari de Matemàtiques i Aplicacions de Castelló)
Vindel, Pura (Institut Universitari de Matemàtiques i Aplicacions de Castelló)

Date:	2018
Abstract:	In this paper, we study the dynamical behaviour of the Chebyshev--Halley family applied on a family of degree n polynomials. For n=2 we bound the set of parameters for which the iterative methods have convergence regions which do not correspond to the basins of attraction of the roots. We also study the dynamics of indifferent fixed points on the boundary of the regions of parameters with bad behaviour. Finally, we provide a numerical study on the boundedness of the regions of parameters with bad behaviour for the family of degree n polynomials.
Grants:	Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P Ministerio de Economía y Competitividad MTM2014-55580-REDT
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Communications in nonlinear science and numerical simulation, Vol. 56 (March 2018) , p. 508-525, ISSN 1007-5704

DOI: 10.1016/j.cnsns.2017.08.024

Postprint 25 p, 4.7 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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