• Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains 

      Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (1) (Journal of Mathematical Chemistry, 08/2017)
      We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead ...
    • Extending the Applicability of Stirling's Method 

      Amorós, Cristina (1); Argyros, Ioannis K; Magreñán, Á. Alberto; Regmi, Samundra; González-Crespo, Rubén (1); Sicilia, Juan Antonio (1) (Mathematics, 01/2020)
      Stirling's method is considered as an alternative to Newton's method when the latter fails to converge to a solution of a nonlinear equation. Both methods converge quadratically under similar convergence criteria and require ...
    • 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 mesh independence for solving nonlinear equations using restricted domains 

      Argyros, Ioannis K; Sheth, Soham M.; Younis, Rami M.; Magreñán, Á. Alberto (1); George, Santhosh (International Journal of Applied and Computational Mathematics, 12/2017)
      The mesh independence principle states that, if Newton’s method is used to solve an equation on Banach spaces as well as finite dimensional discretizations of that equation, then the behaviour of the discretized process ...
    • New Improvement of the Domain of Parameters for Newton’s Method 

      Amorós, Cristina (1); Argyros, Ioannis K; González, Daniel; Magreñán, Á. Alberto; Regmi, Samundra; Sarría, Íñigo (1) (Mathematics, 01/2020)
      There is a need to extend the convergence domain of iterative methods for computing a locally unique solution of Banach space valued operator equations. This is because the domain is small in general, limiting the applicability ...
    • Starting points for Newton’s method under a center Lipschitz condition for the second derivative 

      Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (1) (Journal of Computational and Applied Mathematics, 03/2018)
      We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose ...