• 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 ...
    • 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 ...
    • 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 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 ...
    • New semilocal and local convergence analysis for the Secant method 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K (Applied Mathematics and Computation, 06/2015)
      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 ...
    • 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 ...
    • Secant-like methods for solving nonlinear models with applications to chemistry 

      Magreñán, Á. Alberto (1); Argyros, Ioannis K; Orcos, Lara (1) (Journal of Mathematical Chemistry, 2017)
      We present a local as well a semilocal convergence analysis of secant-like methods under g eneral conditions in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The new ...