Mostrando ítems 1-15 de 15

    • 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 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 efficient parametric family of iterative methods for solving nonlinear systems 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Journal of Difference Equations and Applications, 18/09/2019)
      A bi-parametric family of iterative schemes for solving nonlinear systems is presented. We prove for any value of parameters the sixth-order of convergence of any members of the class. The efficiency and computational ...
    • 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 ...
    • Convergence and dynamics of a higher order family of iterative methods 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we study the convergence as well as the dynamics of some high convergence order family of iterative methods.
    • Convergence of iterative methods for multiple zeros 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we study the convergence, as well as the dynamics, of some high order family of iterative methods
    • Convergence planes of iterative methods 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we study the convergence planes associated to a certain class of iterative methods.
    • Funciones Peso para Métodos de Resolución de Ecuaciones no Lineales con Raíces Múltiples 

      Contreras-Ossa, Rafael Andrés (23/09/2020)
      Existen numerosos métodos iterativos para la resolución de ecuaciones no lineales de la forma 𝑓(𝑥) = 0. En particular, los casos con raíces múltiples requieren de sus propias soluciones. En este trabajo proponemos ...
    • Highly efficient family of iterative methods for solving nonlinear models 

      Behl, Ramandeep; Sarría, Íñigo (1); González-Crespo, Rubén (1); Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 15/01/2019)
      In this study, we present a new highly efficient sixth-order family of iterative methods for solving nonlinear equations along with convergence properties. Further, we extend this family to the multidimensional case ...
    • 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 ...
    • On the improvement of the order of convergence of iterative methods for solving nonlinear systems by means of memory 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus (1); Torregrosa, Juan Ramón (Applied Mathematics Letters, 06/2020)
      Iterative methods with memory for solving nonlinear systems have been designed. For approximating the accelerating parameters the Kurchatov's divided difference is used as an approximation of the derivative of second order. ...
    • 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 study of eighth-order iterative methods for solving nonlinear equations 

      Cordero, Alicia; Magreñán, Á. Alberto (1); Quemada, Carlos; Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2016)
      In this paper, we study the stability of the rational function associated to a known family of eighth-order iterative schemes on quadratic polynomials. The asymptotic behavior of the fixed points corresponding to the ...