A first overview on the real dynamics of Chebyshev's method
- García-Olivo, M. 1
- Gutiérrez, J.M. 2
- Magreñán, Á.A. 3
- 1 Department of Mathematics, Instituto Tecnológico de Santo Domingo, Dominican Republic
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2
Universidad de La Rioja
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3
Universidad Internacional de La Rioja
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ISSN: 0377-0427
Any de publicació: 2017
Volum: 313
Número: 1
Pàgines: 422-432
Tipus: Article
beta Ver similares en nube de resultadosAltres publicacions en: Journal of Computational and Applied Mathematics
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Resum
In this paper we explore some properties of the well known root-finding Chebyshev's method applied to polynomials defined on the real field. In particular we are interested in showing the existence of extraneous fixed points, that is fixed points of the iteration map that are not root of the considered polynomial. The existence of such extraneous fixed points is a specific property in the dynamical study of Chebyshev's method that does not happen in other known iterative methods as Newton's or Halley's methods. In addition, in this work we consider other dynamical aspects of the method as, for instance, the Feigenbaum bifurcation diagrams or the parameter plane. © 2016 Elsevier B.V.