Mostrando ítems 1-20 de 28

    • 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 for Steffensen-type fourth-order methods 

      Argyros, Ioannis K; George, Santhosh (International Journal of Interactive Multimedia and Artificial Intelligence (IJIMAI), 2015)
      We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier ...
    • 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 ...
    • Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations 

      Magreñán, Á. Alberto (1); 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 ...
    • 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 ...
    • Gauss-Newton method 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
      In this chapter we present the local convergence analysis of Gauss–Newton method using the idea of restricted convergence domains, which allows us to improve previous results. Finally, some special cases and a numerical ...
    • 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.
    • 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 an Improved Jarratt-type Method in Banach Space 

      Argyros, Ioannis K; González, Daniel (International Journal of Interactive Multimedia and Artificial Intelligence (IJIMAI), 2015)
      We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are ...
    • 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 fourth and fifth order parametric family of iterative methods in Banach spaces 

      Maroju, P; Magreñán, Á. Alberto; Sarría, Íñigo (1); Kumar, Abhimanyu (Journal of Mathematical Chemistry, 01/2020)
      This paper deal with the study of local convergence of fourth and fifth order iterative method for solving nonlinear equations in Banach spaces. Only the premise that the first order Frechet derivative fulfills the Lipschitz ...
    • 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 ...