Enlarging the convergence domain of secant-like methods for equations
Argyros, Ioannis K
Ezquerro, J A
Hernández-Verón, M A
Magreñán, Á. Alberto (UNIR)
Tipo de Ítem:Articulo Revista Indexada
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 method and other popular methods as special cases. The convergence analysis is based on our idea of recurrent functions. Using more precise majorizing sequences than before we obtain weaker convergence criteria. These advantages are obtained because we use more precise estimates for the upper bounds on the norm of the inverse of the linear operators involved than in earlier studies. Numerical examples are given to illustrate the advantages of the new approaches.
Este ítem aparece en la(s) siguiente(s) colección(es)
Mostrando ítems relacionados por Título, autor o materia.
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 (UNIR) (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 ...
Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (UNIR) (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 ...
Argyros, Ioannis K; Magreñán, Á. Alberto (UNIR); Orcos, Lara (UNIR); Sicilia, Juan Antonio (UNIR) (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 ...