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A general semilocal convergence result for Newton’s methodunder centered conditions for the second derivative

Published online by Cambridge University Press:  31 July 2012

José Antonio Ezquerro
Affiliation:
University of La Rioja, Department of Mathematics and Computation, C/ Luis de Ulloa s/n, 26004 Logroño, Spain. @unirioja.es
Daniel González
Affiliation:
University of La Rioja, Department of Mathematics and Computation, C/ Luis de Ulloa s/n, 26004 Logroño, Spain. @unirioja.es
Miguel Ángel Hernández
Affiliation:
University of La Rioja, Department of Mathematics and Computation, C/ Luis de Ulloa s/n, 26004 Logroño, Spain. @unirioja.es
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2012

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