• A first overview on the real dynamics of Chebyshev's method 

      García-Olivo, Martín; Gutiérrez, José M; Magreñán, Á. Alberto (1) (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 ...
    • A new tool to study real dynamics: The convergence plane 

      Magreñán, Á. Alberto (1) (Applied Mathematics and Computation, 12/2014)
      In this paper, the author presents a graphical tool that allows to study the real dynamics of iterative methods whose iterations depends on one parameter in an easy and compact way. This tool gives the information as ...
    • On the behavior of chebyshev's method applied to cubic polynomials 

      Magreñán, Á. Alberto (1); 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 (1); 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 ...