• A new fourth-order family for solving nonlinear problems and its dynamics 

      Cordero, Alicia; Feng, Licheng; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 03/2015)
      In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made ...
    • 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 ...
    • Improving the Dynamics of Steffensen-type Methods 

      Amat, Sergio; Busquier, Sonia; Magreñán, Á. Alberto (1) (Applied Mathematics and Information Sciences, 2015)
      The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the ...
    • On the election of the damped parameter of a two-step relaxed Newton-type method 

      Amat, Sergio; Busquier, Sonia; Bermúdez, Concepción; Magreñán, Á. Alberto (1) (Nonlineard Dynamics, 04/2016)
      In this paper, we are interested to justified two typical hypotheses that appear in the convergence analysis, |λ|≤2|λ|≤2 and z0z0 sufficient close to z∗z∗ . In order to proof these ideas, the dynamics of a damped ...
    • 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 ...
    • Stability analysis of a parametric family of iterative methods for solving nonlinear models 

      Cordero, Alicia; Gutiérrez, José M; Magreñán, Á. Alberto (1); 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 ...