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Listar por autor "Gutiérrez, José M"

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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 ...

    • Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane 

      Magreñán, Á. Alberto ; Cordero, Alicia; Gutiérrez, José M; Torregrosa, Juan Ramón (Mathematics and Computers in Simulation, 11/2014)
      The real dynamics of a family of fourth-order iterative methods is studied when it is applied on quadratic polynomials. A Scaling Theorem is obtained and the conjugacy classes are analyzed. The convergence plane is used ...

    • Stability analysis of a parametric family of iterative methods for solving nonlinear models 

      Cordero, Alicia; Gutiérrez, José M; Magreñán, Á. Alberto ; Torregrosa, Juan Ramón (Applied Mathematics and Computation, 07/2016)
      A one-parametric family of fourth-order iterative methods for solving nonlinear systems is presented, proving the fourth-order of convergence of all members in this family, except one of them whose order is five. The methods ...