Year: 2015
Author: Ioannis K. Argyros, Santhosh George
Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 362–374
Abstract
We present a local convergence analysis for higher order methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies, Taylor expansions and hypotheses on higher order Fréchet-derivatives are used. We expand the applicability of these methods using only hypotheses on the first Fréchet derivative. Moreover, we obtain a radius of convergence and computable error bounds using Lipschitz constants not given before. Numerical examples are also presented in this study.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v48n4.15.04
Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 362–374
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Higher order method Banach space Fréchet derivative local convergence.