• 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 ...
    • 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 convergence of a higher order family of methods and its dynamics 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2017)
      In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some ...
    • On the convergence of an optimal fourth-order family of methods and its dynamics 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Applied Mathematics and Computation, 02/2015)
      In this paper, we present the study of the semilocal and local convergence of an optimal fourth-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials ...
    • 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 ...
    • Optimal Fourth-Order Weerakoon–Fernando-Type Methods for Multiple Roots and Their Dynamics 

      Chand, Prem Bahadur; Chicharro, Francisco Israel (1); Jain, Pankaj; Sethi, Kriti (Mediterranean Journal of Mathematics, 16/04/2019)
      In this paper, we present optimal fourth-order methods for finding multiple roots of non-linear equations, where the multiplicity is known in advance. These methods are based on the third-order method given by Weerakoon ...
    • 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 ...
    • Stability and applicability of iterative methods with memory 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 15/03/2019)
      Based on the third-order Traub’s method, two iterative schemes with memory are introduced. The proper inclusion of accelerating parameters allows the introduction of memory. Therefore, the order of convergence of the ...