• 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 ...
    • 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 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 ...
    • 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 ...
    • 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 ...