A Geometrical Approach to Indefinite Least Squares Problems

Autores
Giribet, Juan Ignacio; Maestripieri, Alejandra Laura; Martínez Pería, Francisco Dardo
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given Hilbert spaces ℋ and K , a (bounded) closed range operator C:H→K and a vector y∈K , consider the following indefinite least squares problem: find u∈ℋ such that 〈B(Cu−y),Cu−y〉=min x∈ℋ〈B(Cx−y),Cx−y, where B:K→K is a bounded selfadjoint operator. This work is devoted to give necessary and sufficient conditions for the existence of solutions of this abstract problem. Although the indefinite least squares problem has been thoroughly studied in finite dimensional spaces, the geometrical approach presented in this manuscript is quite different from the analytical techniques used before. As an application we provide some new sufficient conditions for the existence of solutions of an ℋ∞ estimation problem.
Facultad de Ciencias Exactas
Materia
Matemática
Ciencias Exactas
Least squares
Oblique projections
Selfadjoint operators
Weighted generalized inverses
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/141580
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/141580
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling A Geometrical Approach to Indefinite Least Squares ProblemsGiribet, Juan IgnacioMaestripieri, Alejandra LauraMartínez Pería, Francisco DardoMatemáticaCiencias ExactasLeast squaresOblique projectionsSelfadjoint operatorsWeighted generalized inversesGiven Hilbert spaces ℋ and K , a (bounded) closed range operator C:H→K and a vector y∈K , consider the following indefinite least squares problem: find u∈ℋ such that 〈B(Cu−y),Cu−y〉=min x∈ℋ〈B(Cx−y),Cx−y, where B:K→K is a bounded selfadjoint operator. This work is devoted to give necessary and sufficient conditions for the existence of solutions of this abstract problem. Although the indefinite least squares problem has been thoroughly studied in finite dimensional spaces, the geometrical approach presented in this manuscript is quite different from the analytical techniques used before. As an application we provide some new sufficient conditions for the existence of solutions of an ℋ∞ estimation problem.Facultad de Ciencias Exactas2009-06-20info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf65-81http://sedici.unlp.edu.ar/handle/10915/141580enginfo:eu-repo/semantics/altIdentifier/issn/0167-8019info:eu-repo/semantics/altIdentifier/issn/1572-9036info:eu-repo/semantics/altIdentifier/doi/10.1007/s10440-009-9532-3info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T11:04:18Zoai:sedici.unlp.edu.ar:10915/141580Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 11:04:18.494SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv A Geometrical Approach to Indefinite Least Squares Problems
title A Geometrical Approach to Indefinite Least Squares Problems
spellingShingle A Geometrical Approach to Indefinite Least Squares Problems
Giribet, Juan Ignacio
Matemática
Ciencias Exactas
Least squares
Oblique projections
Selfadjoint operators
Weighted generalized inverses
title_short A Geometrical Approach to Indefinite Least Squares Problems
title_full A Geometrical Approach to Indefinite Least Squares Problems
title_fullStr A Geometrical Approach to Indefinite Least Squares Problems
title_full_unstemmed A Geometrical Approach to Indefinite Least Squares Problems
title_sort A Geometrical Approach to Indefinite Least Squares Problems
dc.creator.none.fl_str_mv Giribet, Juan Ignacio
Maestripieri, Alejandra Laura
Martínez Pería, Francisco Dardo
author Giribet, Juan Ignacio
author_facet Giribet, Juan Ignacio
Maestripieri, Alejandra Laura
Martínez Pería, Francisco Dardo
author_role author
author2 Maestripieri, Alejandra Laura
Martínez Pería, Francisco Dardo
author2_role author
author
dc.subject.none.fl_str_mv Matemática
Ciencias Exactas
Least squares
Oblique projections
Selfadjoint operators
Weighted generalized inverses
topic Matemática
Ciencias Exactas
Least squares
Oblique projections
Selfadjoint operators
Weighted generalized inverses
dc.description.none.fl_txt_mv Given Hilbert spaces ℋ and K , a (bounded) closed range operator C:H→K and a vector y∈K , consider the following indefinite least squares problem: find u∈ℋ such that 〈B(Cu−y),Cu−y〉=min x∈ℋ〈B(Cx−y),Cx−y, where B:K→K is a bounded selfadjoint operator. This work is devoted to give necessary and sufficient conditions for the existence of solutions of this abstract problem. Although the indefinite least squares problem has been thoroughly studied in finite dimensional spaces, the geometrical approach presented in this manuscript is quite different from the analytical techniques used before. As an application we provide some new sufficient conditions for the existence of solutions of an ℋ∞ estimation problem.
Facultad de Ciencias Exactas
description Given Hilbert spaces ℋ and K , a (bounded) closed range operator C:H→K and a vector y∈K , consider the following indefinite least squares problem: find u∈ℋ such that 〈B(Cu−y),Cu−y〉=min x∈ℋ〈B(Cx−y),Cx−y, where B:K→K is a bounded selfadjoint operator. This work is devoted to give necessary and sufficient conditions for the existence of solutions of this abstract problem. Although the indefinite least squares problem has been thoroughly studied in finite dimensional spaces, the geometrical approach presented in this manuscript is quite different from the analytical techniques used before. As an application we provide some new sufficient conditions for the existence of solutions of an ℋ∞ estimation problem.
publishDate 2009
dc.date.none.fl_str_mv 2009-06-20
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/141580
url http://sedici.unlp.edu.ar/handle/10915/141580
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0167-8019
info:eu-repo/semantics/altIdentifier/issn/1572-9036
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10440-009-9532-3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
65-81
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 13.13397

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