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hammerstein’s integral equation

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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1 results

A general semilocal convergence result for Newton’s methodunder centered conditions for the second derivative
José Antonio Ezquerro, Daniel González, Miguel Ángel Hernández
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 1 / January 2013

Published online by Cambridge University Press:

31 July 2012, pp. 149-167

Print publication:

January 2013
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From Kantorovich’s theory we present a semilocal convergence result for Newton’s methodwhich is based mainly on a modification of the condition required to the second derivativeof the operator involved. In particular, instead of requiring that the second derivativeis bounded, we demand that it is centered. As a consequence, we obtain a modification ofthe starting points for Newton’s method. We illustrate this study with applications tononlinear integral equations of mixed Hammerstein type.