Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations

Detalhes bibliográficos
Autor(a) principal: Cezaro, Adriano de
Data de Publicação: 2011
Outros Autores: Baumeister, Johann, Leitão, Antônio
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da FURG (RI FURG)
Texto Completo: http://repositorio.furg.br/handle/1/854
Resumo: We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the case of noisy data we propose a modi_cation, the so called loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation parameters is introduced and a di_erent stopping rule is used. Convergence analysis for this method is also provided.
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spelling Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equationsNonlinear systemsIll-posed equationsRegularizationIterated Tikhonov methodKaczmarz methodWe investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the case of noisy data we propose a modi_cation, the so called loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation parameters is introduced and a di_erent stopping rule is used. Convergence analysis for this method is also provided.2011-08-16T12:45:31Z2011-08-16T12:45:31Z2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfCEZARO, Adriano de; BAUMEISTER, Johann; LEITÃO, Antonio. Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations. Inverse Problems and Imaging, v. 5, n. 1, p. 1-17, 2011. Disponível em:<http://www.mtm.ufsc.br/~aleitao/public/reprints/pap2011-bcl-IPI.pdf>. Acesso em: 15 ago. 2011.1930-8337http://repositorio.furg.br/handle/1/85410.3934/ipi.2011.5engCezaro, Adriano deBaumeister, JohannLeitão, Antônioinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da FURG (RI FURG)instname:Universidade Federal do Rio Grande (FURG)instacron:FURG2023-03-28T11:34:34Zoai:repositorio.furg.br:1/854Repositório InstitucionalPUBhttps://repositorio.furg.br/oai/request || http://200.19.254.174/oai/requestopendoar:2023-03-28T11:34:34Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG)false
dc.title.none.fl_str_mv Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
title Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
spellingShingle Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
Cezaro, Adriano de
Nonlinear systems
Ill-posed equations
Regularization
Iterated Tikhonov method
Kaczmarz method
title_short Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
title_full Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
title_fullStr Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
title_full_unstemmed Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
title_sort Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
author Cezaro, Adriano de
author_facet Cezaro, Adriano de
Baumeister, Johann
Leitão, Antônio
author_role author
author2 Baumeister, Johann
Leitão, Antônio
author2_role author
author
dc.contributor.author.fl_str_mv Cezaro, Adriano de
Baumeister, Johann
Leitão, Antônio
dc.subject.por.fl_str_mv Nonlinear systems
Ill-posed equations
Regularization
Iterated Tikhonov method
Kaczmarz method
topic Nonlinear systems
Ill-posed equations
Regularization
Iterated Tikhonov method
Kaczmarz method
description We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the case of noisy data we propose a modi_cation, the so called loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation parameters is introduced and a di_erent stopping rule is used. Convergence analysis for this method is also provided.
publishDate 2011
dc.date.none.fl_str_mv 2011-08-16T12:45:31Z
2011-08-16T12:45:31Z
2011
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv CEZARO, Adriano de; BAUMEISTER, Johann; LEITÃO, Antonio. Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations. Inverse Problems and Imaging, v. 5, n. 1, p. 1-17, 2011. Disponível em:<http://www.mtm.ufsc.br/~aleitao/public/reprints/pap2011-bcl-IPI.pdf>. Acesso em: 15 ago. 2011.
1930-8337
http://repositorio.furg.br/handle/1/854
10.3934/ipi.2011.5
identifier_str_mv CEZARO, Adriano de; BAUMEISTER, Johann; LEITÃO, Antonio. Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations. Inverse Problems and Imaging, v. 5, n. 1, p. 1-17, 2011. Disponível em:<http://www.mtm.ufsc.br/~aleitao/public/reprints/pap2011-bcl-IPI.pdf>. Acesso em: 15 ago. 2011.
1930-8337
10.3934/ipi.2011.5
url http://repositorio.furg.br/handle/1/854
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.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:Repositório Institucional da FURG (RI FURG)
instname:Universidade Federal do Rio Grande (FURG)
instacron:FURG
instname_str Universidade Federal do Rio Grande (FURG)
instacron_str FURG
institution FURG
reponame_str Repositório Institucional da FURG (RI FURG)
collection Repositório Institucional da FURG (RI FURG)
repository.name.fl_str_mv Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG)
repository.mail.fl_str_mv
_version_ 1807384393193357312

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