Mostrando ítems 1-11 de 11

    • Different methods for solving STEM problems 

      Argyros, Ioannis K; Magreñán, Á. Alberto; Orcos, Lara (1); Sarría, Íñigo (1); Sicilia, Juan Antonio (1) (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 ...
    • Domain of parameters 

      Magreñán, Á. Alberto (1); 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 ...
    • 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 ...
    • Extending the convergence domain of the Secant and Moser method in Banach Space 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 12/2015)
      We present a new semilocal convergence analysis for the Secant and the Moser method in order to approximate a solution of an equation in a Banach space setting. Using the method of recurrent relations and weaker sufficient ...
    • Extending the domain of starting points for Newton's method under conditions on the second derivative 

      Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 10/2018)
      In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we ...
    • Generalized equations 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we present some developments for the local convergence of Newton's method. Some special cases and a numerical example illuminating the theoretical results are also presented.
    • Newton's method 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      The center Lipschitz condition is used in this chapter, together with the Lipschitz condition, in order to obtain weaker convergence criteria to ensure the convergence pf Newton's method. Numerical examples and applications ...
    • Newton's method for solving optimal shape design problems 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we present some results related to Newton's method in order to extend the solvability of optimal shape design problems. Moreover, some numerical examples are also presented in the chapter.
    • Newton's method to solve equations with solutions of multiplicity greater than one 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter the solvability of equations with multiple roots is expanded using the modified Newton's method. Examples are also presented illuminating the theoretical results.
    • The majorization method in the Kantorovich theory 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      The goal in this chapter is to present some improvements related to the convergence of Newton's and modified Newton's method by means of introducing and using the center Lipschitz condition. Using both conditions we obtain ...
    • Unified local convergence for newton's method and uniqueness of the solution of equations under generalized conditions in a Banach space 

      Argyros, Ioannis K; Magreñán, Á. Alberto; Orcos, Lara (1); Sarría, Íñigo (1) (Mathematics, 05/2019)
      Under the hypotheses that a function and its Frechet derivative satisfy some generalized Newton-Mysovskii conditions, precise estimates on the radii of the convergence balls of Newton's method, and of the uniqueness ball ...