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Listar por autor "Hernández-Verón, M A"
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Comparing of the behaviour of iterative methods based on different means
Amat, Sergio; Busquier, Sonia; Hernández-Verón, M A; Magreñán, Á. Alberto; Orcos, Lara (AIP Conference Proceedings, 2020)Based on the modification of family of iterative processes of Chebyshev-Halley presented by M. Kansal et al. in [2], whose convergence is cubic, we will present in this talk a comparison between the behaviour of some members ... -
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 (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 ... -
Enlarging the convergence domain of secant-like methods for equations
Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Hilout, S; Magreñán, Á. Alberto (Taiwanese Journal of Mathematics, 04/2015)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 ... -
Extending the domain of starting points for Newton's method under conditions on the second derivative
Argyros, Ioannis K; Ezquerro, J A; Hernández-Verón, M A; Magreñán, Á. Alberto (Journal of Computational and Applied Mathematics, 10/2018)In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we ... -
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 (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 ... -
Toward a general theory of point to point iterative processes free of derivatives with quadratic convergence
Hernández-Verón, M A; Magreñán, Á. Alberto ; Rubio, María Jesús (AIP Conference Proceedings, 2018)In this work, we are concerned with the problem of developing a general theory about derivative-free iterative procedures with quadratic convergence. Newton's method is the most used, well-known and studied in order to ...