• 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: ...
    • 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 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 ...
    • 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 ...
    • On the convergence of a Damped Secant method with modified right-hand side vector 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Applied Mathematics and Computation, 02/2015)
      We present a convergence analysis for a Damped Secant 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 case ...
    • On the convergence of a higher order family of methods and its dynamics 

      Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (1); Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2017)
      In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some ...
    • On the convergence of an optimal fourth-order family of methods and its dynamics 

      Argyros, Ioannis K; Magreñán, Á. Alberto (1) (Applied Mathematics and Computation, 02/2015)
      In this paper, we present the study of the semilocal and local convergence of an optimal fourth-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials ...