Mostrando ítems 1-20 de 20

    • 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 ...
    • Comparing of the behaviour of iterative methods based on different means 

      Amat, Sergio; Busquier, Sonia; Hernández-Verón, M A; Magreñán, Á. Alberto; Orcos, Lara (1) (AIP Conference Proceedings, 2020)
      Based on the modification of family of iterative processes of Chebyshev-Halley presented by M. Kansal et al. in [2], whose convergence is cubic, we will present in this talk a comparison between the behaviour of some members ...
    • 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 ...
    • 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 ...
    • Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators 

      Amat, Sergio; Busquier, Sonia; Bermúdez, Concepción; Magreñán, Á. Alberto (1) (Algorithms, 09/2015)
      This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution ...
    • Expanding the applicability of the Secant method under weaker conditions 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Applied Mathematics and Computation, 09/2015)
      We present a new semilocal convergence analysis for Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on ...
    • Expanding the convergence domain for Chun-Stanica-Neta family of third order methods in banach spaces 

      Argyros, Ioannis K; Santhosh, George; Magreñán, Á. Alberto (1) (Journal of the Korean Mathematical Society, 01/2015)
      We present a semilocal convergence analysis of a third order method for approximating a locally unique solution of an equation in a Banach space setting. Recently, this method was studied by Chun, Stanica. and Neta. These ...
    • Extending the convergence domain of Newton's method for twice Frechet differentiable operators 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Analysis and Applications, 03/2016)
      We present a semi-local convergence analysis of Newton's method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Using center-Lipschitz condition on the first and the ...
    • 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 ...
    • Improved convergence analysis for Newton-like methods 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Numerical Algorithms, 04/2016)
      We present a new semilocal convergence analysis for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in ...
    • Improved semilocal convergence analysis in Banach space with applications to chemistry 

      Argyros, Ioannis K; Giménez de Ory, Elena (1); Magreñán, Á. Alberto (1) (Journal of Mathematical Chemistry, 2017)
      We present a new semilocal convergence analysis for Secant methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds ...
    • Multistep modified Newton-Hermitian and Skew-Hermitian Splitting method 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      Newton–Hermitian and Skew-Hermitian Splitting (MMN-HSS) method.
    • New improved convergence analysis for Newton-like methods with applications 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K; Sicilia, Juan Antonio (1) (Journal of Mathematical Chemistry, 08/2017)
      We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases ...
    • 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.
    • On the convergence of inexact two-point Newton-like methods on Banach spaces 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Applied Mathematics and Computation, 08/2015)
      We present a unified convergence analysis of Inexact Newton like methods in order to approximate a locally unique solution of a nonlinear operator equation containing a nondifferentiable term in a Banach space setting. The ...
    • Optimizing the applicability of a theorem by F. Potra for Newton-like methods 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Applied Mathematics and Computation, 09/2014)
      We present a new sufficient semilocal convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these ...
    • Relaxed secant-type methods 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Nonlinear Studies, 06/2014)
      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 the computation ...
    • Starting points for Newton’s method under a center Lipschitz condition for the second derivative 

      Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 03/2018)
      We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose ...