• A multidimensional dynamical approach to iterative methods with memory 

      Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura Elsevier (2015-11-15)
      A dynamical approach on the dynamics of iterative methods with memory for solving nonlinear equations is made. We have designed new methods with memory from Steffensen’ or Traub’s schemes, as well as from a parametric ...
    • openAccess   Behaviour of fixed and critical points of the (α, c) −family of iterative methods 

      Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura Springer Verlag (2015-01)
      In this paper we study the dynamical behavior of the (α, c ) -family of itera- tive methods for solving nonlinear equations, when we apply the fixed point operator associated to this family on quadratic polynomials. ...
    • openAccess   Bulbs of Period Two in the Family of Chebyshev-Halley Iterative Methods on Quadratic Polynomials 

      Vindel, Pura; Torregrosa, Juan R.; Cordero Barbero, Alicia Hindawi (2013)
      The parameter space associated to the parametric family of Chebyshev-Halley on quadratic polynomials shows a dynamical richness worthy of study. This analysis has been initiated by the authors in previous works. Every value ...
    • openAccess   Chaos  in  King's  iterative  family   

      Cordero Barbero, Alicia; García Maimó, Javier; Torregrosa, Juan R.; Vassileva, Maria P.; Vindel, Pura Elsevier (2013-08)
      In this paper, the dynamics of King’s family of iterative schemes for solving nonlinear equations is studied. The parameter spaces are presented, showing the complexity of the family. The analysis of the parameter space ...
    • openAccess   Dynamical Analysis to Explain the NumericalAnomalies in the Family of Ermakov-KalitkinType Methods 

      Cordero, Alicia; Torregrosa, Juan R.; Vindel, Pura Vilnius Gediminas Technical University (VGTU) Press (2019)
      In this paper, we study the dynamics of an iterative method based onthe Ermakov-Kalitkin class of iterative schemes for solving nonlinear equations. Asit was proven in ”A new family of iterative methods widening areas of ...
    • openAccess   Dynamics of a family of Chebyshev-Halley 

      Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura Elsevier (2013-04-15)
      In this paper, the dynamics of the Chebyshev–Halley family is studied on quadratic polynomials. A singular set, that we call cat set, appears in the parameter space associated to the family. This set has interesting ...
    • openAccess   Dynamics of a multipoint variant of Chebyshev–Halley’s family 

      Vindel, Pura; Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa, Juan R. Elsevier (2016)
      In this paper, a complex dynamical study of a parametric Chebyshev–Halley type family of iterative methods on quadratic polynomial is presented. The stability of the fixed points is analyzed in terms of the parameter of ...
    • openAccess   Dynamics of the family of c-iterative methods 

      Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura Taylor & Francis (2014-02-21)
      In this paper, the dynamics of the family of c-iterative methods for solving nonlinear equations are studied on quadratic polynomials. A singular parameter space is presented to show the complexity of the family. The ...
    • openAccess   Period-doubling bifurcations in the family of Chebyshev–Halley-type methods 

      Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura Taylor & Francis (2013)
      The choice of a member of a parametric family of iterative methods is not always easy. The family of Chebyshev–Halley schemes is a good example of it. The analysis of bifurcation points of this family allows us to define ...
    • openAccess   Stability of King’s family of iterative methods with memory 

      Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura Elsevier (2017-07)
      In the literature exist many iterative methods with memory for solving nonlinear equations, the most of them designed in the last years. As they use the information of (at least) the two previous iterates to generate the ...
    • openAccess   Study of a Biparametric Family of Iterative Methods 

      Campos, Beatriz; Cordero Barbero, Alicia; Magreñán Ruiz, Ángel Alberto; Torregrosa, Juan R.; Vindel, Pura Hindawi Publishing Corporation (2014-12-24)
      Thedynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the 𝑐������-iterative methods and the well-known Chebyshev-Halley family.We find ...
    • openAccess   Study of the dynamics of third-order iterative methods on quadratic polynomials 

      Cordero Barbero, Alicia; Torregrosa, Juan R.; Vindel, Pura Taylor & Francis (2012)
      In this paper, we analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods, for solving nonlinear equations, applied on second-degree complex ...