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A complex dynamical approach of Chebyshev’s method
García-Olivo, Martín; Gutiérrez, José M; Magreñán, Á. Alberto (SeMA Journal, 11/2015)The aim of this paper is to investigate the iterative root-finding Chebyshev’s method from a dynamical perspective. We analyze the behavior of the method applied to low degree polynomials. In this work we focus on the ... -
A first overview on the real dynamics of Chebyshev's method
García-Olivo, Martín; Gutiérrez, José M; Magreñán, Á. Alberto (Journal of Computational and Applied Mathematics, 07/2017)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 ... -
On the behavior of chebyshev's method applied to cubic polynomials
Magreñán, Á. Alberto ; García-Olivo, Martín; Gutiérrez, José M (Civil-Comp Proceedings, 2014)This paper shows the dynamical behavior of the well-known Chebyshev method when it is applied to cubic polynomials. We present the scaling theorem associated to the method and we study the real dynamics of the method. The ...