5 research outputs found
Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces
We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations.
The recurrence relations for the method are derived, and then an existence-uniqueness theorem is given to establish the
R-order of the method to be five and a priori error bounds. Finally, a numerical application is presented to demonstrate
our approach
Semilocal convergence by using recurrence relations for fifth-order method in Banach spaces
In this paper, a semilocal convergence result in Banach spaces of an efficient fifth-order method is analyzed. Recurrence relations are used in order to prove this convergence, and some a priori error bounds are found. This scheme is finally used to estimate the solution of an integral equation and so, the theoretical results are numerically checked. We use this example to show the better efficiency of the current method compared with other existing ones, including Newton's scheme.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-{01,02}.Cordero Barbero, A.; Hernandez-Veron, MA.; Romero, N.; Torregrosa Sánchez, JR. (2015). Semilocal convergence by using recurrence relations for fifth-order method in Banach spaces. Journal of Computational and Applied Mathematics. 273:205-213. https://doi.org/10.1016/j.cam.2014.06.008S20521327
Estudio sobre convergencia y dinámica de los métodos de Newton, Stirling y alto orden
Las matemáticas, desde el origen de esta ciencia, han estado al servicio de la
sociedad tratando de dar respuesta a los problemas que surgÃan. Hoy en dÃa sigue
siendo asÃ, el desarrollo de las matemáticas está ligado a la demanda de otras
ciencias que necesitan dar solución a situaciones concretas y reales.
La mayorÃa de los problemas de ciencia e ingenierÃa no pueden resolverse
usando ecuaciones lineales, es por tanto que hay que recurrir a las ecuaciones no
lineales para modelizar dichos problemas (Amat, 2008; véase también Argyros y
Magreñán, 2017, 2018), entre otros. El conflicto que presentan las ecuaciones no
lineales es que solo en unos pocos casos es posible encontrar una solución única,
por tanto, en la mayor parte de los casos, para resolverlas hay que recurrir a los
métodos iterativos. Los métodos iterativos generan, a partir de un punto inicial,
una sucesión que puede converger o no a la solución
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described