Mostrando ítems 1-13 de 13

    • A complex dynamical approach of Chebyshev’s method 

      García-Olivo, Martín; Gutiérrez, José M; Magreñán, Á. Alberto (1) (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 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 ...
    • CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Martínez, Tobias H. (1); Torregrosa, Juan Ramón (Journal of Mathematical Chemistry, 03/2020)
      The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative methods ...
    • Family of Multiple-Root Finding Iterative Methods Based on Weight Functions 

      Chicharro, Francisco Israel (1); Contreras, Rafael Andrés (1); Garrido, Neus (1) (MathematicsMDPI, 09/12/2020)
      A straightforward family of one-point multiple-root iterative methods is introduced. The family is generated using the technique of weight functions. The order of convergence of the family is determined in its convergence ...
    • 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 ...
    • Introduction to complex dynamics 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter some dynamical concepts of complex dynamics that will be used in this book are presented. Moreover, some graphics illustrating the theoretical concepts are shown in order to let the reader understand them better.
    • 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 design and analysis of high order Weerakoon-Fernando methods based on weight functions 

      Chand, Prem Bahadur; Chicharro, Francisco Israel; Jain, Pankaj (Computational and Mathematical Methods, 18/06/2020)
      In this article, using the idea of weight functions on Weerakoon‐Fernando's method, an optimal fourth‐order method and some higher order multipoint methods for solving nonlinear equations are proposed. These methods are ...
    • 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 ...