A first overview on the real dynamics of Chebyshev’s method

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• 作者：M. Garcí ; a-Olivo<sup>asup><sup> ; sup><sup>martin1matdr@hotmail.comsup> ; José ; M. Gutié ; rrez<sup>bsup><sup> ; sup><sup>jmguti@unirioja.essup> ; Á ; .A. Magreñ ; á ; n<sup>csup><sup> ; sup><sup>alberto.magrenan@unir.netsup>
• 关键词：primary ; 65P99
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：422-432
• 全文大小：1559 K
• 卷排序：318

文摘

In this paper we explore some properties of the well known root-finding Chebyshev&rsquo;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&rsquo;s method that does not happen in other known iterative methods as Newton&rsquo;s or Halley&rsquo;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.