Regularization methods for ill-posed problems in multiple Hilbert scales

Autores
Mazzieri, Gisela Luciana; Spies, Ruben Daniel
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, and regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases, convergence is proved and orders and optimal orders of convergence are shown. Finally, some potential applications and open problems are discussed.
Fil: Mazzieri, Gisela Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; Argentina
Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Materia
REGULARIZATION
MULTIPLE HILBERT SCALES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/273855
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Regularization methods for ill-posed problems in multiple Hilbert scalesMazzieri, Gisela LucianaSpies, Ruben DanielREGULARIZATIONMULTIPLE HILBERT SCALEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, and regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases, convergence is proved and orders and optimal orders of convergence are shown. Finally, some potential applications and open problems are discussed.Fil: Mazzieri, Gisela Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; ArgentinaFil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaIOP Publishing2012-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/273855Mazzieri, Gisela Luciana; Spies, Ruben Daniel; Regularization methods for ill-posed problems in multiple Hilbert scales; IOP Publishing; Inverse Problems; 28; 5; 5-2012; 1-300266-5611CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/0266-5611/28/5/055005info:eu-repo/semantics/altIdentifier/doi/10.1088/0266-5611/28/5/055005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-26T08:39:38Zoai:ri.conicet.gov.ar:11336/273855instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-26 08:39:39.023CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Regularization methods for ill-posed problems in multiple Hilbert scales
title Regularization methods for ill-posed problems in multiple Hilbert scales
spellingShingle Regularization methods for ill-posed problems in multiple Hilbert scales
Mazzieri, Gisela Luciana
REGULARIZATION
MULTIPLE HILBERT SCALES
title_short Regularization methods for ill-posed problems in multiple Hilbert scales
title_full Regularization methods for ill-posed problems in multiple Hilbert scales
title_fullStr Regularization methods for ill-posed problems in multiple Hilbert scales
title_full_unstemmed Regularization methods for ill-posed problems in multiple Hilbert scales
title_sort Regularization methods for ill-posed problems in multiple Hilbert scales
dc.creator.none.fl_str_mv Mazzieri, Gisela Luciana
Spies, Ruben Daniel
author Mazzieri, Gisela Luciana
author_facet Mazzieri, Gisela Luciana
Spies, Ruben Daniel
author_role author
author2 Spies, Ruben Daniel
author2_role author
dc.subject.none.fl_str_mv REGULARIZATION
MULTIPLE HILBERT SCALES
topic REGULARIZATION
MULTIPLE HILBERT SCALES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, and regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases, convergence is proved and orders and optimal orders of convergence are shown. Finally, some potential applications and open problems are discussed.
Fil: Mazzieri, Gisela Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; Argentina
Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
description Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, and regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases, convergence is proved and orders and optimal orders of convergence are shown. Finally, some potential applications and open problems are discussed.
publishDate 2012
dc.date.none.fl_str_mv 2012-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/273855
Mazzieri, Gisela Luciana; Spies, Ruben Daniel; Regularization methods for ill-posed problems in multiple Hilbert scales; IOP Publishing; Inverse Problems; 28; 5; 5-2012; 1-30
0266-5611
CONICET Digital
CONICET
url http://hdl.handle.net/11336/273855
identifier_str_mv Mazzieri, Gisela Luciana; Spies, Ruben Daniel; Regularization methods for ill-posed problems in multiple Hilbert scales; IOP Publishing; Inverse Problems; 28; 5; 5-2012; 1-30
0266-5611
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/0266-5611/28/5/055005
info:eu-repo/semantics/altIdentifier/doi/10.1088/0266-5611/28/5/055005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.011256

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