Multiplicative Lidskii's inequalities and optimal perturbations of frames

Autores
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F={fj}j∈In for Cd we compute those dual frames G of F that are optimal perturbations of the canonical dual frame for F under certain restrictions on the norms of the elements of G. On the other hand, we compute those V⋅F={Vfj}j∈In – for invertible operators V which are close to the identity – that are optimal perturbations of F. That is, we compute the optimal perturbations of F among frames G={gj}j∈In that have the same linear relations as F. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.
Fil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Materia
CONVEX POTENTIALS
FRAMES
LIDSKII'S INEQUALITY
MAJORIZATION
PERTURBATION OF FRAMES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/2672
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/2672
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Multiplicative Lidskii's inequalities and optimal perturbations of framesMassey, Pedro GustavoRuiz, Mariano AndresStojanoff, DemetrioCONVEX POTENTIALSFRAMESLIDSKII'S INEQUALITYMAJORIZATIONPERTURBATION OF FRAMEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F={fj}j∈In for Cd we compute those dual frames G of F that are optimal perturbations of the canonical dual frame for F under certain restrictions on the norms of the elements of G. On the other hand, we compute those V⋅F={Vfj}j∈In – for invertible operators V which are close to the identity – that are optimal perturbations of F. That is, we compute the optimal perturbations of F among frames G={gj}j∈In that have the same linear relations as F. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.Fil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaFil: Ruiz, Mariano Andres. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaFil: Stojanoff, Demetrio. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaElsevier Science Inc.2015-03-15info: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/11336/2672Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Multiplicative Lidskii's inequalities and optimal perturbations of frames; Elsevier Science Inc.; Linear Algebra And Its Applications; 469; 15-3-2015; 539-5680024-3795enginfo:eu-repo/semantics/altIdentifier/url/http://goo.gl/xNx2CJinfo:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1405.4277info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2014.12.004info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:07:06Zoai:ri.conicet.gov.ar:11336/2672instacron: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:34982025-10-22 12:07:06.99CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multiplicative Lidskii's inequalities and optimal perturbations of frames
title Multiplicative Lidskii's inequalities and optimal perturbations of frames
spellingShingle Multiplicative Lidskii's inequalities and optimal perturbations of frames
Massey, Pedro Gustavo
CONVEX POTENTIALS
FRAMES
LIDSKII'S INEQUALITY
MAJORIZATION
PERTURBATION OF FRAMES
title_short Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_full Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_fullStr Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_full_unstemmed Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_sort Multiplicative Lidskii's inequalities and optimal perturbations of frames
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author_role author
author2 Ruiz, Mariano Andres
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv CONVEX POTENTIALS
FRAMES
LIDSKII'S INEQUALITY
MAJORIZATION
PERTURBATION OF FRAMES
topic CONVEX POTENTIALS
FRAMES
LIDSKII'S INEQUALITY
MAJORIZATION
PERTURBATION OF FRAMES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F={fj}j∈In for Cd we compute those dual frames G of F that are optimal perturbations of the canonical dual frame for F under certain restrictions on the norms of the elements of G. On the other hand, we compute those V⋅F={Vfj}j∈In – for invertible operators V which are close to the identity – that are optimal perturbations of F. That is, we compute the optimal perturbations of F among frames G={gj}j∈In that have the same linear relations as F. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.
Fil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
description In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F={fj}j∈In for Cd we compute those dual frames G of F that are optimal perturbations of the canonical dual frame for F under certain restrictions on the norms of the elements of G. On the other hand, we compute those V⋅F={Vfj}j∈In – for invertible operators V which are close to the identity – that are optimal perturbations of F. That is, we compute the optimal perturbations of F among frames G={gj}j∈In that have the same linear relations as F. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.
publishDate 2015
dc.date.none.fl_str_mv 2015-03-15
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/11336/2672
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Multiplicative Lidskii's inequalities and optimal perturbations of frames; Elsevier Science Inc.; Linear Algebra And Its Applications; 469; 15-3-2015; 539-568
0024-3795
url http://hdl.handle.net/11336/2672
identifier_str_mv Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Multiplicative Lidskii's inequalities and optimal perturbations of frames; Elsevier Science Inc.; Linear Algebra And Its Applications; 469; 15-3-2015; 539-568
0024-3795
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://goo.gl/xNx2CJ
info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1405.4277
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2014.12.004
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
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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score 12.982451

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