Mostrando ítems 1-20 de 155

    • 3D visualization through the hologram for the learning of area and volume concepts 

      Orcos, Lara ; Jordán, Cristina; Magreñán, Á. Alberto (Mathematics, 26/02/2019)
      This study aims to implement and evaluate a methodological proposal using the hologram as a teaching medium for the learning of concepts related to areas and volumes of geometrical bodies. The study has been carried out ...
    • A biparametric extension of King’s fourth-order methods and their dynamics 

      Geum, Young Hee; Kim, Young Ik; Magreñán, Á. Alberto (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 complex dynamical approach of Chebyshev’s method 

      García-Olivo, Martín; Gutiérrez, José M; Magreñán, Á. Alberto (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 contemporary study of iterative methods: Convergence, dynamics and applications 

      Magreñán, Á. Alberto ; 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 (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 ; 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 technique for studying the convergence of Newton’s solver with real life applications 

      Argyros, Ioannis K; Magreñán, Á. Alberto; Yáñez, Dionisio F.; Sicilia, Juan Antonio (Journal of Mathematical Chemistry, 04/2020)
      The convergence domain for both the local and semilocal case of Newton’s method for Banach space valued operators is small in general. There is a plethora of articles that have extended the convergence criterion due to ...
    • A new tool to study real dynamics: The convergence plane 

      Magreñán, Á. Alberto (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 ; Martínez-Álvarez, Isabel ; Muelas, Álvaro ; Pradas Montilla, Silvia ; Magreñán, Á. Alberto (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 (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 (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 (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 ; Mahdiani, K; Rainer, J Javier (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 ...
    • Advances in the Semilocal Convergence of Newton's Method with Real-World Applications 

      Argyros, Ioannis K; Magreñán, Á. Alberto; Orcos, Lara; Sarría, Íñigo (Mathematics, 24/03/2019)
      The aim of this paper is to present a new semi-local convergence analysis for Newton's method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies ...
    • An efficient optimal family of sixteenth order methods for nonlinear models 

      Behl, Ramandeep; Amat, Sergio; Magreñán, Á. Alberto ; 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 ; Orcos, Lara (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 comparison between frozen Potra and Schmidt-Schwetlick schemes with dynamical analysis 

      Argyros, Michael I; Argyros, Ioannis K; González, Daniel; Magreñán, Á. Alberto; Moysi, Alejandro; Sarría, Íñigo (Computational and Mathematical Methods, 2021)
      In this article, we propose a new research related to the convergence of the frozen Potra and Schmidt-Schwetlick schemes when we apply to equations. The purpose of this study is to introduce a comparison between two solutions ...
    • Ball convergence for eighth order method 

      Argyros, Ioannis K; Magreñán, Á. Alberto (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 ; Argyros, Ioannis K; Rainer, J Javier ; Sicilia, Juan Antonio (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 ...
    • Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (SeMA Journal, 11/2015)
      We study the local convergence of a method presented by Cordero et al. of convergence order at least five to approximate a locally unique solution of a nonlinear equation. These studies show the convergence under hypotheses ...