Mostrando ítems 1-20 de 106

    • 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 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 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 ...
    • 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 ...
    • 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 ...
    • Convergence and dynamics of a higher order family of iterative methods 

      Magreñán, Á. Alberto ; 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 and Dynamics of a Higher-Order Method 

      Moysi, Alejandro; Argyros, Ioannis K; Regmi, Samundra; González, Daniel; Magreñán, Á. Alberto; Sicilia, Juan Antonio (Symmetry, 03/2020)
      Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves ...
    • Convergence and the dynamics of Chebyshev-Halley type methods 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we present a weak convergence analysis and the dynamics of Chebyshev–Halley type methods.
    • Convergence of iterative methods for multiple zeros 

      Magreñán, Á. Alberto ; 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 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 (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 ...
    • Convergence planes of iterative methods 

      Magreñán, Á. Alberto ; 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.
    • Developments on the convergence of some iterative methods 

      Argyros, Ioannis K; Magreñán, Á. Alberto ; Sicilia, Juan Antonio (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 ...
    • Different methods for solving STEM problems 

      Argyros, Ioannis K; Magreñán, Á. Alberto; Orcos, Lara ; Sarría, Íñigo ; Sicilia, Juan Antonio (Journal of Mathematical Chemistry, 05/2019)
      We first present a local convergence analysis for some families of fourth and six order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies have used ...
    • Directional Newton methods 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter, we are concerned with the convergence of the Directional Newton method (DNM), which is used in many areas such us computer graphics and many applied sciences. We obtain weaker convergence criteria, larger ...
    • Directional newton methods and restricted domains 

      Argyros, Ioannis K; Magreñán, Á. Alberto (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 ...
    • Domain of parameters 

      Magreñán, Á. Alberto ; Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we present several convergence results related to Newton's method in which we enlarge the domain of parameters, which is one of the main problems in iterative procedure studies. Moreover, several numerical ...