• 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 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 ...
    • Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability 

      Chicharro, Francisco Israel (1); Cordero, Alicia; Garrido, Neus; Torregrosa, Juan Ramón (Axioms, 06/05/2019)
      In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing ...
    • 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 ...
    • Second derivative free sixth order continuation method for solving nonlinear equations with applications 

      Maroju, P; Magreñán, Á. Alberto (1); Motsa, S S; Sarría, Íñigo (1) (Journal of Mathematical Chemistry, 08/2018)
      In this paper, we deal with the study of convergence analysis of modified parameter based family of second derivative free continuation method for solving nonlinear equations. We obtain the order of convergence is at least ...
    • 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 ...
    • Third-degree anomalies of Traub's method 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2017)
      Traub’s method is a tough competitor of Newton’s scheme for solving nonlinear equations as well as nonlinear systems. Due to its third-order convergence and its low computational cost, it is a good procedure to be applied ...