We present new semilocal convergence conditions for a two-step Newton-like projection method of Lavrentiev regularization for solving ill-posed equations in a Hilbert space setting. The new convergence conditions are weaker than in earlier studies. Examples are presented to show that older convergence conditions are not satisfied but the new conditions are satisfied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am40-3-7,
author = {Ioannis K. Argyros and Santhosh George},
title = {On the semilocal convergence of a two-step Newton-like projection method for ill-posed equations},
journal = {Applicationes Mathematicae},
volume = {40},
year = {2013},
pages = {367-382},
zbl = {1296.65081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-3-7}
}
Ioannis K. Argyros; Santhosh George. On the semilocal convergence of a two-step Newton-like projection method for ill-posed equations. Applicationes Mathematicae, Tome 40 (2013) pp. 367-382. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-3-7/