Mostrando ítems 1-20 de 99

    • A biparametric extension of King’s fourth-order methods and their dynamics 

      Geum, Young Hee; Kim, Young Ik; Magreñán, Á. Alberto (1) (Applied Mathematics and Computation, 05/2016)
      A class of two-point quartic-order simple-zero finders and their dynamics are investigated in this paper by extending King’s fourth-order family of methods. With the introduction of an error corrector having a weight ...
    • A contemporary study of iterative methods: Convergence, dynamics and applications 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Elsevier, 2018)
      A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, ...
    • 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 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 ...
    • A study of 16 years old student learning strategies from a neuropsychological perspective: An intervention proposal 

      Martín-Lobo, Pilar (1); Martínez-Álvarez, Isabel (1); Muelas, Álvaro (1); Pradas Montilla, Silvia (1); Magreñán, Á. Alberto (1) (Trends in Neuroscience and Education, 06/2018)
      Scientific achievements related to brain processes provide innovation and improvements in students' learning. The aim of this study was to analyse, relate, and compare learning strategies and academic performance of students ...
    • A study of dynamics via Mobius conjugacy map on a family of sixth-order modified Newton-like multiple-zero finders with bivariate polynomial weight functions 

      Geum, Young Hee; Kim, Young Ik; Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 15/12/2018)
      A generic family of sixth-order modified Newton-like multiple-zero finders have been proposed in Geum et al. (2016). Among them we select a specific family of iterative methods with uniparametric bivariate polynomial weight ...
    • A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Numerical Algorithms, 01/2016)
      We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and Bailey ...
    • A unified convergence analysis for secant-type methods 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Journal of the Korean Mathematical Society, 11/2014)
      We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes he computation ...
    • A variant of Steffensen-King's type family with accelerated sixth-order convergence and high efficiency index: Dynamic study and approach 

      Lotfi, T; Magreñán, Á. Alberto (1); Mahdiani, K; Rainer, J Javier (1) (Applied Mathematics and Computation, 02/2015)
      First, it is attempted to derive an optimal derivative-free Steffensen-King's type family without memory for computing a simple zero of a nonlinear function with efficiency index 4(1/3) approximate to 1.587. Next, since ...
    • An efficient optimal family of sixteenth order methods for nonlinear models 

      Behl, Ramandeep; Amat, Sergio; Magreñán, Á. Alberto (1); Motsa, S S (Journal of Computational and Applied Mathematics, 2018)
      The principle aim of this manuscript is to propose a general scheme that can be applied to any optimal iteration function of order eight whose first substep employ Newton’s method to further develop new interesting optimal ...
    • An Overview on Steffensen-Type Methods 

      Amat, Sergio; Busquier, Sonia; Magreñán, Á. Alberto (1); Orcos, Lara (1) (Advances in iterative methods for nonlinear equations, 2016)
      In this chapter we present an extensive overview of Steffensen-type methods. We first present the real study of the methods and then we present the complex dynamics related this type of methods applied to different ...
    • Ball convergence for eighth order method 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a ...
    • Ball convergence of a sixth-order Newton-like method based on means under weak conditions 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K; Rainer, J Javier (1); Sicilia, Juan Antonio (1) (Journal of Mathematical Chemistry, 08/2018)
      We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative ...
    • Complexity of an Homotopy Method at the Neighbourhood of a Zero 

      Yakoubsohn, J. C.; Gutierrez, J. M.; Magreñán, Á. Alberto (1) (Advances in iterative methods for nonlinear equations, 2016)
      This paper deals with the enlargement of the region of convergence of Newton's method for solving nonlinear equations defined in Banach spaces. We have used an homotopy method to obtain approximate zeros of the considered ...
    • Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains 

      Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (1) (Journal of Mathematical Chemistry, 08/2017)
      We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead ...
    • Decision model for siting transport and logistic facilities in urban environments: A methodological approach 

      Frailea, Alberto; Larrodé, Emilio; Magreñán, Á. Alberto (1); Sicilia, Juan Antonio (1) (Journal of Computational and Applied Mathematics, 01/2016)
      In this study, based on the use of a geographic information system (GIS), we define a decision model for determining the possible optimal locations of various facilities in an urban setting, which can be used by the transport ...
    • Developments on the convergence of some iterative methods 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1); Sicilia, Juan Antonio (1) (Optimization and Dynamics with Their Applications: Essays in Honor of Ferenc Szidarovszky, 2017)
      Iterative methods, play an important role in computational sciences. In this chapter, we present new semilocal and local convergence results for the Newton-Kantorovich method. These new results extend the applicability of ...
    • Directional newton methods and restricted domains 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Iterative Methods and Their Dynamics with Applications: A Contemporary Study, 2017)
      Let F : D ⊂ ℝn → ℝ be a differentiable function. In computer graphics, we often need to compute and display the intersection C = A ⋂ B of two surfaces A and B in ℝ3 [5], [6]. If the two surfaces are explicitly given by A ...
    • Enlarging the convergence domain of secant-like methods for equations 

      Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Hilout, S; Magreñán, Á. Alberto (1) (Taiwanese Journal of Mathematics, 04/2015)
      We present two new semilocal convergence analyses for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. These methods include the secant, Newton's ...