On the Gauss-Newton method for solving equations

We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved...

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Detalles Bibliográficos
Autores: Argyros,Ioaniss K, Hitlout,Saïd
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:Chile
Institución:Agencia Nacional de Investigación y Desarrollo
Repositorio:SciELO Chile
OAI Identifier:oai:scielo:S0716-09172012000100002
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100002
Access Level:acceso abierto
Palabra clave:Gauss-Newton method
semilocal convergence
Frechet- derivative
Lipschitz/center-Lipschitz condition
convergence domain
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spelling On the Gauss-Newton method for solving equationsArgyros,Ioaniss KHitlout,SaïdGauss-Newton methodsemilocal convergenceFrechet- derivativeLipschitz/center-Lipschitz conditionconvergence domainWe use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss- Newton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solutionUniversidad Católica del Norte, Departamento de Matemáticas2012-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100002Proyecciones (Antofagasta) v.31 n.1 2012reponame:SciELO Chileinstname:Agencia Nacional de Investigación y Desarrolloinstacron:ANID-SciELO Chileen10.4067/S0716-09172012000100002info:eu-repo/semantics/openAccessinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2012-04-13T00:00:00Zoai:scielo:S0716-09172012000100002opendoar:2012-04-13T00:00falseopendoar:2012-04-13T00:00SciELO Chile - Agencia Nacional de Investigación y Desarrollofalse
dc.title.none.fl_str_mv On the Gauss-Newton method for solving equations
title On the Gauss-Newton method for solving equations
spellingShingle On the Gauss-Newton method for solving equations
Argyros,Ioaniss K
Gauss-Newton method
semilocal convergence
Frechet- derivative
Lipschitz/center-Lipschitz condition
convergence domain
title_short On the Gauss-Newton method for solving equations
title_full On the Gauss-Newton method for solving equations
title_fullStr On the Gauss-Newton method for solving equations
title_full_unstemmed On the Gauss-Newton method for solving equations
title_sort On the Gauss-Newton method for solving equations
dc.creator.none.fl_str_mv Argyros,Ioaniss K
Hitlout,Saïd
author Argyros,Ioaniss K
author_facet Argyros,Ioaniss K
Hitlout,Saïd
author_role author
author2 Hitlout,Saïd
author2_role author
dc.subject.none.fl_str_mv Gauss-Newton method
semilocal convergence
Frechet- derivative
Lipschitz/center-Lipschitz condition
convergence domain
topic Gauss-Newton method
semilocal convergence
Frechet- derivative
Lipschitz/center-Lipschitz condition
convergence domain
description We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss- Newton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solution
publishDate 2012
dc.date.none.fl_str_mv 2012-03-01
dc.type.*.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.none.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.none.fl_str_mv http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100002
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dc.language.none.fl_str_mv en
language_invalid_str_mv en
dc.relation.none.fl_str_mv 10.4067/S0716-09172012000100002
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Universidad Católica del Norte, Departamento de Matemáticas
publisher.none.fl_str_mv Universidad Católica del Norte, Departamento de Matemáticas
dc.source.none.fl_str_mv Proyecciones (Antofagasta) v.31 n.1 2012
reponame:SciELO Chile
instname:Agencia Nacional de Investigación y Desarrollo
instacron:ANID-SciELO Chile
instname_str Agencia Nacional de Investigación y Desarrollo
instacron_str ANID-SciELO Chile
institution ANID-SciELO Chile
reponame_str SciELO Chile
collection SciELO Chile
repository.name.fl_str_mv SciELO Chile - Agencia Nacional de Investigación y Desarrollo
repository.mail.fl_str_mv
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score 15.30478

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