Expanding the applicability
of two-point Newton-like methods
under generalized conditions
Applicationes Mathematicae, Tome 40 (2013) no. 1, pp. 63-90
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied.
Keywords:
two point newton like method approximate locally unique solution nonlinear equation containing non differentiable term banach space setting using precise majorizing sequences earlier studies present tighter semi local local convergence analysis weaker convergence criteria expand applicability these methods numerical examples provided where old convergence criteria convergence criteria satisfied
Affiliations des auteurs :
Ioannis K. Argyros 1 ; Saïd Hilout 2
@article{10_4064_am40_1_4,
author = {Ioannis K. Argyros and Sa{\"\i}d Hilout},
title = {Expanding the applicability
of two-point {Newton-like} methods
under generalized conditions},
journal = {Applicationes Mathematicae},
pages = {63--90},
year = {2013},
volume = {40},
number = {1},
doi = {10.4064/am40-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am40-1-4/}
}
TY - JOUR AU - Ioannis K. Argyros AU - Saïd Hilout TI - Expanding the applicability of two-point Newton-like methods under generalized conditions JO - Applicationes Mathematicae PY - 2013 SP - 63 EP - 90 VL - 40 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/am40-1-4/ DO - 10.4064/am40-1-4 LA - en ID - 10_4064_am40_1_4 ER -
%0 Journal Article %A Ioannis K. Argyros %A Saïd Hilout %T Expanding the applicability of two-point Newton-like methods under generalized conditions %J Applicationes Mathematicae %D 2013 %P 63-90 %V 40 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/am40-1-4/ %R 10.4064/am40-1-4 %G en %F 10_4064_am40_1_4
Ioannis K. Argyros; Saïd Hilout. Expanding the applicability of two-point Newton-like methods under generalized conditions. Applicationes Mathematicae, Tome 40 (2013) no. 1, pp. 63-90. doi: 10.4064/am40-1-4
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