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

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...

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Detalles Bibliográficos
Autores: Ezquerro, J.A. [0000-0001-8120-167X], González, D. [0000-0001-5282-7251], Hernández, M. [0000-0001-5478-2958]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:España
Institución:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc691db750603269e8157f
Acceso en línea:https://investigacion.unirioja.es/documentos/5bbc691db750603269e8157f
Access Level:acceso abierto
Palabra clave:A priori error estimates
Hammerstein’s integral equation
Majorizing sequence
Newton’s method
Semilocal convergence
The Newton—Kantorovich theorem
Descripción
Sumario: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