On the convergence of Newton's method under $\omega ^\star $-conditioned second derivative
Applicationes Mathematicae, Tome 38 (2011) no. 3, pp. 341-355
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We provide a new semilocal result for the quadratic convergence of Newton's method under $\omega ^\star $-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using $\omega $-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.
Keywords:
provide semilocal result quadratic convergence newtons method under omega star conditioned second chet derivative banach space handle equations where usual lipschitz type conditions verifiable application involving nonlinear integral equations boundary value problems provided turns out similar result using omega conditioned hypotheses provide usable error estimates indicating only linear convergence newtons method
Affiliations des auteurs :
Ioannis K. Argyros 1 ; Saïd Hilout 2
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author = {Ioannis K. Argyros and Sa{\"\i}d Hilout},
title = {On the convergence of {Newton's} method under $\omega ^\star $-conditioned second derivative},
journal = {Applicationes Mathematicae},
pages = {341--355},
year = {2011},
volume = {38},
number = {3},
doi = {10.4064/am38-3-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am38-3-5/}
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%0 Journal Article %A Ioannis K. Argyros %A Saïd Hilout %T On the convergence of Newton's method under $\omega ^\star $-conditioned second derivative %J Applicationes Mathematicae %D 2011 %P 341-355 %V 38 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/am38-3-5/ %R 10.4064/am38-3-5 %G en %F 10_4064_am38_3_5
Ioannis K. Argyros; Saïd Hilout. On the convergence of Newton's method under $\omega ^\star $-conditioned second derivative. Applicationes Mathematicae, Tome 38 (2011) no. 3, pp. 341-355. doi: 10.4064/am38-3-5
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