Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation
Argyros, Ioannis K
Magreñán, Á. Alberto (UNIR)
Orcos, Lara (UNIR)
Tipo de Ítem:Articulo Revista Indexada
We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the sense of Traub. In earlier studies such as Steffensen (Scand Actuar J 16(1):64–72, 1933) and Zafer et al. (Sci World J, 2015. doi:10.1155/2015/934260) the convergence was based on hypotheses on the third derivative or even higher. We extend the applicability of theses methods using only the first derivative. Moreover, we provide computable radii and error bounds based on Lipschitz constants. Furthermore, the dynamics of this method are studied in order to find the best choice of the parameter in terms of convergence. An application is also presented in this study.
Este ítem aparece en la(s) siguiente(s) colección(es)
Mostrando ítems relacionados por Título, autor o materia.
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 ...
Magreñán, Á. Alberto (UNIR); Argyros, Ioannis K; Orcos, Lara (UNIR) (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 ...
Orcos, Lara (UNIR); Magreñán, Á. Alberto (UNIR) (International Journal of Learning Technology, 2018)The aim of the work presented in this article is to assess whether the use of a hologram enhances the meaningful learning of cellular division contents. A pilot phase has been carried out with a sample of students of 4th ...