Mostrando ítems 1-20 de 27

    • 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 ...
    • Advances in the Semilocal Convergence of Newton's Method with Real-World Applications 

      Argyros, Ioannis K; Magreñán, Á. Alberto; Orcos, Lara; Sarría, Iñigo (1) (Mathematics, 24/03/2019)
      The aim of this paper is to present a new semi-local convergence analysis for Newton's method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies ...
    • Different methods for solving STEM problems 

      Argyros, Ioannis K; Magreñán, Á. Alberto; Orcos, Lara (1); Sarría, Iñigo (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 ...
    • Expanding the aplicability of secant method with applications 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Bulletin of the Korean Mathematical Society, 05/2015)
      We present new sufficient convergence criteria for the convergence of the secant-method to a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center Lipschitz instead of just ...
    • 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 applicability of the local and semilocal convergence of Newton's method 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Applied Mathematics and Computation, 01/2017)
      We present a local as well a semilocal convergence analysis for Newton's method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton's method as follows: ...
    • 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 ...
    • 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 ...
    • Improving the domain of parameters for Newton's method with applications 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1); Sicilia, Juan Antonio (1) (Journal of Computational and Applied Mathematics, 07/2017)
      We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are ...
    • 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 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 a relaxed two-step Newton like method with applications 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1); Orcos, Lara (1); Sicilia, Juan Antonio (1) (Journal of Mathematical Chemistry, 08/2017)
      We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fr,chet derivative ...
    • 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 ...
    • New improved convergence analysis for the secant method 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Mathematics and Computers in Simulation, 01/2016)
      We present a new convergence analysis, for the secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz ...
    • On the convergence of a damped Newton-like method with modified right hand side vector 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Applied Mathematics and Computation, 09/2015)
      We present a convergence analysis for a damped Newton like method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special ...