Ball Convergence for Higher Order Methods Under Weak Conditions

Ball Convergence for Higher Order Methods Under Weak Conditions

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.

Author Details

Ioannis K. Argyros

Santhosh George