Mostrando ítems 1-19 de 19

    • A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (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 (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 ...
    • Ball convergence of a sixth-order Newton-like method based on means under weak conditions 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K; Rainer, J Javier (1); Sicilia, Juan Antonio (1) (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 ...
    • 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 ...
    • Extended local convergence for some inexact methods with applications 

      Argyros, Ioannis K; Legaz, M. J.; Magreñán, Á. Alberto; Moreno, D.; Sicilia, Juan Antonio (1) (Journal of Mathematical Chemistry, 05/2019)
      We present local convergence results for inexact iterative procedures of high convergence order in a normed space in order to approximate a locally unique solution. The hypotheses involve only Lipschitz conditions on the ...
    • 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 local convergence analysis of the Gauss-Newton method under a majorant condition 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Computational Optimization and Applications, 03/2015)
      We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97-118, 2008), ...
    • 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 ...
    • Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1); Orcos, Lara (1) (Journal of Mathematical Chemistry, 08/2016)
      We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the ...
    • Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions 

      Amat, Sergio (1); Argyros, Ioannis K; Busquier, Sonia; Magreñán, Á. Alberto (1) (Numerical Algorithms, 02/2017)
      We present a local convergence analysis of a two-point four parameter Jarratt-like method of high convergence order in order to approximate a locally unique solution of a nonlinear equation. In contrast to earlier studies ...
    • Local Convergence and the Dynamics of a Two-Step Newton-Like Method 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 05/2016)
      We present the local convergence analysis and the study of the dynamics of a two-step Newton-like method in order to approximate a locally unique solution of multiplicity one of a nonlinear equation.
    • Local convergence for multi-point-parametric Chebyshev–Halley-type methods of high 

      Argyros, Ioannis K; George, Santhosh; Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 07/2015)
      We present a local convergence analysis for general multi-point-Chebyshev-Halley-type methods (MMCHTM) of high convergence order in order to approximate a solution of an equation in a Banach space setting. MMCHTM includes ...
    • Local Convergence of the Gauss-Newton Method for Infective-Overdetermined Systems 

      Amat, Sergio; Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Journal of the Korean Mathematical Society, 09/2014)
      We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information ...
    • 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 ...
    • 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 ...
    • On the local convergence and the dynamics of Chebyshev–Halley methods with six and eight order of convergence 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Journal of Computational and Applied Mathematics, 05/2016)
      We study the local convergence of Chebyshev–Halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation. In Sharma (2015) (see Theorem 1, p. 121) the convergence ...
    • 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 ...
    • Study of a high order family: Local convergence and dynamics 

      Amorós, Cristina (1); Argyros, Ioannis K; González-Crespo, Rubén (1); Magreñán, Á. Alberto; Orcos, Lara (1); Sarría, Iñigo (1) (Mathematics, 01/03/2019)
      The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a ...
    • 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, Iñigo (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 ...