Two-step Newton methods

We present sufficient convergence conditions for two-step Newton methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of our approach over other studies such as Argyros et al. (2010) [5], Chen et al. (2010) [11], Ezquerro et al....

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Authors: Magreñán Ruiz, Á.A. [0000-0002-6991-5706], Argyros, I.K.
Format: article
Status:Published version
Publication Date:2014
Country:España
Institution:Universidad de La Rioja (UR)
Repository:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc69f2b750603269e82433
Online Access:https://investigacion.unirioja.es/documentos/5bbc69f2b750603269e82433
Access Level:Open access
Keyword:Banach space
Kantorovich hypothesis
Local convergence
Majorizing sequence
Semilocal convergence
Two-step Newton method
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spelling Two-step Newton methodsMagreñán Ruiz, Á.A. [0000-0002-6991-5706]Argyros, I.K.Banach spaceKantorovich hypothesisLocal convergenceMajorizing sequenceSemilocal convergenceTwo-step Newton methodWe present sufficient convergence conditions for two-step Newton methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of our approach over other studies such as Argyros et al. (2010) [5], Chen et al. (2010) [11], Ezquerro et al. (2000) [16], Ezquerro et al. (2009) [15], Hernández and Romero (2005) [18], Kantorovich and Akilov (1982) [19], Parida and Gupta (2007) [21], Potra (1982) [23], Proinov (2010) [25], Traub (1964) [26] for the semilocal convergence case are: weaker sufficient convergence conditions, more precise error bounds on the distances involved and at least as precise information on the location of the solution. In the local convergence case more precise error estimates are presented. These advantages are obtained under the same computational cost as in the earlier stated studies. Numerical examples involving Hammerstein nonlinear integral equations where the older convergence conditions are not satisfied but the new conditions are satisfied are also presented in this study for the semilocal convergence case. In the local case, numerical examples and a larger convergence ball are obtained. © 2013 Elsevier Inc. All rights reserved.2014info:eu-repo/semantics/articleSubtype: Articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://investigacion.unirioja.es/documentos/5bbc69f2b750603269e82433reponame:RIUR. Repositorio Institucional de la Universidad de La Riojainstname:Universidad de La Rioja (UR)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.1016/J.JCO.2013.10.002info:eu-repo/semantics/altIdentifier/wos/WOS:000337864100008info:eu-repo/semantics/altIdentifier/pissn/0885-064XTwo-step Newton methods, 2014, vol. 30, núm. 4, pág. 533-553info:eu-repo/semantics/openAccessoai:portal.dialnet.es:doc/5bbc69f2b750603269e824332026-06-14T12:47:17Z
dc.title.none.fl_str_mv Two-step Newton methods
title Two-step Newton methods
spellingShingle Two-step Newton methods
Magreñán Ruiz, Á.A. [0000-0002-6991-5706]
Banach space
Kantorovich hypothesis
Local convergence
Majorizing sequence
Semilocal convergence
Two-step Newton method
title_short Two-step Newton methods
title_full Two-step Newton methods
title_fullStr Two-step Newton methods
title_full_unstemmed Two-step Newton methods
title_sort Two-step Newton methods
dc.creator.none.fl_str_mv Magreñán Ruiz, Á.A. [0000-0002-6991-5706]
Argyros, I.K.
author Magreñán Ruiz, Á.A. [0000-0002-6991-5706]
author_facet Magreñán Ruiz, Á.A. [0000-0002-6991-5706]
Argyros, I.K.
author_role author
author2 Argyros, I.K.
author2_role author
dc.subject.none.fl_str_mv Banach space
Kantorovich hypothesis
Local convergence
Majorizing sequence
Semilocal convergence
Two-step Newton method
topic Banach space
Kantorovich hypothesis
Local convergence
Majorizing sequence
Semilocal convergence
Two-step Newton method
description We present sufficient convergence conditions for two-step Newton methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of our approach over other studies such as Argyros et al. (2010) [5], Chen et al. (2010) [11], Ezquerro et al. (2000) [16], Ezquerro et al. (2009) [15], Hernández and Romero (2005) [18], Kantorovich and Akilov (1982) [19], Parida and Gupta (2007) [21], Potra (1982) [23], Proinov (2010) [25], Traub (1964) [26] for the semilocal convergence case are: weaker sufficient convergence conditions, more precise error bounds on the distances involved and at least as precise information on the location of the solution. In the local convergence case more precise error estimates are presented. These advantages are obtained under the same computational cost as in the earlier stated studies. Numerical examples involving Hammerstein nonlinear integral equations where the older convergence conditions are not satisfied but the new conditions are satisfied are also presented in this study for the semilocal convergence case. In the local case, numerical examples and a larger convergence ball are obtained. © 2013 Elsevier Inc. All rights reserved.
publishDate 2014
dc.date.none.fl_str_mv 2014
dc.type.none.fl_str_mv info:eu-repo/semantics/article
Subtype: Article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://investigacion.unirioja.es/documentos/5bbc69f2b750603269e82433
url https://investigacion.unirioja.es/documentos/5bbc69f2b750603269e82433
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/J.JCO.2013.10.002
info:eu-repo/semantics/altIdentifier/wos/WOS:000337864100008
info:eu-repo/semantics/altIdentifier/pissn/0885-064X
Two-step Newton methods, 2014, vol. 30, núm. 4, pág. 533-553
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:RIUR. Repositorio Institucional de la Universidad de La Rioja
instname:Universidad de La Rioja (UR)
instname_str Universidad de La Rioja (UR)
reponame_str RIUR. Repositorio Institucional de la Universidad de La Rioja
collection RIUR. Repositorio Institucional de la Universidad de La Rioja
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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