We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am30-1-7,
author = {Ioannis K. Argyros},
title = {On the convergence and application of Stirling's method},
journal = {Applicationes Mathematicae},
volume = {30},
year = {2003},
pages = {109-119},
zbl = {1033.65034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-1-7}
}
Ioannis K. Argyros. On the convergence and application of Stirling's method. Applicationes Mathematicae, Tome 30 (2003) pp. 109-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-1-7/