We present a local convergence analysis for a family of iterative methods obtained by using decomposition techniques. The convergence of these methods was shown before using hypotheses on up to the seventh derivative although only the first derivative appears in these methods. In the present study we expand the applicability of these methods by showing convergence using only the first derivative. Moreover we present a radius of convergence and computable error bounds based only on Lipschitz constants. Numerical examples are also provided.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am2261-12-2015,
author = {Ioannis K. Argyros and Santhosh George and Shobha Monnanda Erappa},
title = {Local convergence for a family of iterative methods based on decomposition techniques},
journal = {Applicationes Mathematicae},
volume = {43},
year = {2016},
pages = {133-143},
zbl = {06602766},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am2261-12-2015}
}
Ioannis K. Argyros; Santhosh George; Shobha Monnanda Erappa. Local convergence for a family of iterative methods based on decomposition techniques. Applicationes Mathematicae, Tome 43 (2016) pp. 133-143. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am2261-12-2015/