Weighted least squares solutions of the equation AXB - C = 0
- Autores
- Contino, Maximiliano; Giribet, Juan Ignacio; Maestripieri, Alejandra Laura
- Año de publicación
- 2017
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W ∈ L(H) a positive operator such that W^1/2 is in the p-Schatten class, for some 1 ≤ p < ∞. Given A,B ∈ L(H) with closed range and C ∈ L(H), we study the following weighted approximation problem: analyze the existence ofmin{ ||AXB − C||p,W , X ∈L(H)}, (0.1)where ||X ||p,W = ||W^1/2 X ||p . We also study the related operator approximation problem: analyze the existence ofmin {(AXB − C)*W (AXB − C), X ∈L(H)}, (0.2)where the order is the one induced in L(H) by the cone of positive operators. In this paper we prove that the existence of the minimum of (0.2) is equivalent to the existence of a solution of the normal equation A*W (AXB − C) = 0. We also give sufficient conditions for the existence of the minimum.
Fil: Contino, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina - Materia
-
OBLIQUE PROJECTIONS
OPERATOR APPROXIMATION
SCHATTEN P CLASSES - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/65550
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Weighted least squares solutions of the equation AXB - C = 0Contino, MaximilianoGiribet, Juan IgnacioMaestripieri, Alejandra LauraOBLIQUE PROJECTIONSOPERATOR APPROXIMATIONSCHATTEN P CLASSEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W ∈ L(H) a positive operator such that W^1/2 is in the p-Schatten class, for some 1 ≤ p < ∞. Given A,B ∈ L(H) with closed range and C ∈ L(H), we study the following weighted approximation problem: analyze the existence ofmin{ ||AXB − C||p,W , X ∈L(H)}, (0.1)where ||X ||p,W = ||W^1/2 X ||p . We also study the related operator approximation problem: analyze the existence ofmin {(AXB − C)*W (AXB − C), X ∈L(H)}, (0.2)where the order is the one induced in L(H) by the cone of positive operators. In this paper we prove that the existence of the minimum of (0.2) is equivalent to the existence of a solution of the normal equation A*W (AXB − C) = 0. We also give sufficient conditions for the existence of the minimum.Fil: Contino, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaElsevier Science Inc2017-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/65550Contino, Maximiliano; Giribet, Juan Ignacio; Maestripieri, Alejandra Laura; Weighted least squares solutions of the equation AXB - C = 0; Elsevier Science Inc; Linear Algebra and its Applications; 518; 4-2017; 177-1970024-37951873-1856CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379516306279info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2016.12.028info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1610.00645info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:43:44Zoai:ri.conicet.gov.ar:11336/65550instacron: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:34982025-09-03 09:43:44.964CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Weighted least squares solutions of the equation AXB - C = 0 |
title |
Weighted least squares solutions of the equation AXB - C = 0 |
spellingShingle |
Weighted least squares solutions of the equation AXB - C = 0 Contino, Maximiliano OBLIQUE PROJECTIONS OPERATOR APPROXIMATION SCHATTEN P CLASSES |
title_short |
Weighted least squares solutions of the equation AXB - C = 0 |
title_full |
Weighted least squares solutions of the equation AXB - C = 0 |
title_fullStr |
Weighted least squares solutions of the equation AXB - C = 0 |
title_full_unstemmed |
Weighted least squares solutions of the equation AXB - C = 0 |
title_sort |
Weighted least squares solutions of the equation AXB - C = 0 |
dc.creator.none.fl_str_mv |
Contino, Maximiliano Giribet, Juan Ignacio Maestripieri, Alejandra Laura |
author |
Contino, Maximiliano |
author_facet |
Contino, Maximiliano Giribet, Juan Ignacio Maestripieri, Alejandra Laura |
author_role |
author |
author2 |
Giribet, Juan Ignacio Maestripieri, Alejandra Laura |
author2_role |
author author |
dc.subject.none.fl_str_mv |
OBLIQUE PROJECTIONS OPERATOR APPROXIMATION SCHATTEN P CLASSES |
topic |
OBLIQUE PROJECTIONS OPERATOR APPROXIMATION SCHATTEN P CLASSES |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W ∈ L(H) a positive operator such that W^1/2 is in the p-Schatten class, for some 1 ≤ p < ∞. Given A,B ∈ L(H) with closed range and C ∈ L(H), we study the following weighted approximation problem: analyze the existence ofmin{ ||AXB − C||p,W , X ∈L(H)}, (0.1)where ||X ||p,W = ||W^1/2 X ||p . We also study the related operator approximation problem: analyze the existence ofmin {(AXB − C)*W (AXB − C), X ∈L(H)}, (0.2)where the order is the one induced in L(H) by the cone of positive operators. In this paper we prove that the existence of the minimum of (0.2) is equivalent to the existence of a solution of the normal equation A*W (AXB − C) = 0. We also give sufficient conditions for the existence of the minimum. Fil: Contino, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina |
description |
Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W ∈ L(H) a positive operator such that W^1/2 is in the p-Schatten class, for some 1 ≤ p < ∞. Given A,B ∈ L(H) with closed range and C ∈ L(H), we study the following weighted approximation problem: analyze the existence ofmin{ ||AXB − C||p,W , X ∈L(H)}, (0.1)where ||X ||p,W = ||W^1/2 X ||p . We also study the related operator approximation problem: analyze the existence ofmin {(AXB − C)*W (AXB − C), X ∈L(H)}, (0.2)where the order is the one induced in L(H) by the cone of positive operators. In this paper we prove that the existence of the minimum of (0.2) is equivalent to the existence of a solution of the normal equation A*W (AXB − C) = 0. We also give sufficient conditions for the existence of the minimum. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-04 |
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/11336/65550 Contino, Maximiliano; Giribet, Juan Ignacio; Maestripieri, Alejandra Laura; Weighted least squares solutions of the equation AXB - C = 0; Elsevier Science Inc; Linear Algebra and its Applications; 518; 4-2017; 177-197 0024-3795 1873-1856 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/65550 |
identifier_str_mv |
Contino, Maximiliano; Giribet, Juan Ignacio; Maestripieri, Alejandra Laura; Weighted least squares solutions of the equation AXB - C = 0; Elsevier Science Inc; Linear Algebra and its Applications; 518; 4-2017; 177-197 0024-3795 1873-1856 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379516306279 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2016.12.028 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1610.00645 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Science Inc |
publisher.none.fl_str_mv |
Elsevier Science Inc |
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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1842268619149410304 |
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13.13397 |