ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION

We provide a local convergence analysis for a Newton-type method to approximate a locally unique solution of an operator equation in Banach spaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use in...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	ARGYROS,IOANNIS K, HILOUT,SAÏD
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2008
Materias:	Banach space Newton-type method convergence gamma-type condition local convergence Fréchet-derivative radius of convergence
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000100001
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172008000100001
record_format	dspace
spelling	oai:scielo:S0716-091720080001000012008-05-22ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITIONARGYROS,IOANNIS KHILOUT,SAÏD Banach space Newton-type method convergence gamma-type condition local convergence Fréchet-derivative radius of convergence We provide a local convergence analysis for a Newton-type method to approximate a locally unique solution of an operator equation in Banach spaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use information only at a point and a gamma-type condition [4], [10]. It turns out that our radius of convergence is larger, and more general than the corresponding one in [10]. Moreover the same can hold true when our radius is compared with the ones given in [9] and [11]. A numerical example is also providedinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.27 n.1 20082008-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000100001en10.4067/S0716-09172008000100001
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Banach space Newton-type method convergence gamma-type condition local convergence Fréchet-derivative radius of convergence
spellingShingle	Banach space Newton-type method convergence gamma-type condition local convergence Fréchet-derivative radius of convergence ARGYROS,IOANNIS K HILOUT,SAÏD ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION
description	We provide a local convergence analysis for a Newton-type method to approximate a locally unique solution of an operator equation in Banach spaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use information only at a point and a gamma-type condition [4], [10]. It turns out that our radius of convergence is larger, and more general than the corresponding one in [10]. Moreover the same can hold true when our radius is compared with the ones given in [9] and [11]. A numerical example is also provided
author	ARGYROS,IOANNIS K HILOUT,SAÏD
author_facet	ARGYROS,IOANNIS K HILOUT,SAÏD
author_sort	ARGYROS,IOANNIS K
title	ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION
title_short	ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION
title_full	ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION
title_fullStr	ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION
title_full_unstemmed	ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION
title_sort	on the local convergence of a newton-type method in banach spaces under a gamma-type condition
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2008
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000100001
work_keys_str_mv	AT argyrosioannisk onthelocalconvergenceofanewtontypemethodinbanachspacesunderagammatypecondition AT hiloutsaid onthelocalconvergenceofanewtontypemethodinbanachspacesunderagammatypecondition
_version_	1718439755811651584

ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION

Ejemplares similares