From Kantorovich's theory we present a semilocal convergence result for Newton's method which is based mainly on a modification of the condition required to the second derivative of the operator involved. In particular, instead of requiring that the second derivative is bounded, we demand that it is centered. As a consequence, we obtain a modification of the starting points for Newton's method. We illustrate this study with applications to nonlinear integral equations of mixed Hammerstein type.
@article{M2AN_2013__47_1_149_0,
author = {Ezquerro, Jos\'e Antonio and Gonz\'alez, Daniel and Hern\'andez, Miguel \'Angel},
title = {A general semilocal convergence result for Newton's method under centered conditions for the second derivative},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {149-167},
doi = {10.1051/m2an/2012026},
mrnumber = {2968699},
zbl = {1271.65092},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_1_149_0}
}
Ezquerro, José Antonio; González, Daniel; Hernández, Miguel Ángel. A general semilocal convergence result for Newton's method under centered conditions for the second derivative. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 149-167. doi : 10.1051/m2an/2012026. http://gdmltest.u-ga.fr/item/M2AN_2013__47_1_149_0/
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