| Issue |
ESAIM: M2AN
Volume 47, Number 1, January-February 2013
|
|
|---|---|---|
| Page(s) | 149 - 167 | |
| DOI | https://doi.org/10.1051/m2an/2012026 | |
| Published online | 31 July 2012 | |
A general semilocal convergence result for Newton’s method under centered conditions for the second derivative
University of La Rioja, Department of Mathematics and
Computation, C/ Luis de Ulloa
s/n, 26004
Logroño,
Spain
<jezquer><daniel.gonzalez><mahernan>@unirioja.es
Received:
3
November
2011
Revised:
26
March
2012
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.
Mathematics Subject Classification: 45G10 / 47H99 / 65J15
Key words: Newton’s method / the Newton–Kantorovich theorem / semilocal convergence / majorizing sequence / a priori error estimates / Hammerstein’s integral equation
© EDP Sciences, SMAI, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.