# A general semilocal convergence result for Newton’s method under centered conditions for the second derivative

José Antonio Ezquerro; Daniel González; Miguel Ángel Hernández

- Volume: 47, Issue: 1, page 149-167
- ISSN: 0764-583X

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topEzquerro, José Antonio, González, Daniel, and 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 47.1 (2013): 149-167. <http://eudml.org/doc/273116>.

@article{Ezquerro2013,

abstract = {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.},

author = {Ezquerro, José Antonio, González, Daniel, Hernández, Miguel Ángel},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Newton’s method; the Newton–Kantorovich theorem; semilocal convergence; majorizing sequence; a priori error estimates; Hammerstein’s integral equation; Newton's method; Newton-Kantorovich theorem; Hammerstein's integral equation},

language = {eng},

number = {1},

pages = {149-167},

publisher = {EDP-Sciences},

title = {A general semilocal convergence result for Newton’s method under centered conditions for the second derivative},

url = {http://eudml.org/doc/273116},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Ezquerro, José Antonio

AU - González, Daniel

AU - Hernández, Miguel Ángel

TI - A general semilocal convergence result for Newton’s method under centered conditions for the second derivative

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 1

SP - 149

EP - 167

AB - 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.

LA - eng

KW - Newton’s method; the Newton–Kantorovich theorem; semilocal convergence; majorizing sequence; a priori error estimates; Hammerstein’s integral equation; Newton's method; Newton-Kantorovich theorem; Hammerstein's integral equation

UR - http://eudml.org/doc/273116

ER -

## References

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