A general semilocal convergence result for Newton’s method under centered conditions for the second derivative
- Ezquerro, J.A. 1
- González, D. 1
- Hernández, M. 1
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1
Universidad de La Rioja
info
ISSN: 0764-583X
Ano de publicación: 2013
Volume: 47
Número: 1
Páxinas: 149-167
Tipo: Artigo
Outras publicacións en: Mathematical Modelling and Numerical Analysis
Resumo
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