• 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 ...
    • 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 ...
    • 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 ...