Optimal frame completions

Autores
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a finite sequence of vectors F0 in C d we describe the spectral and geometrical structure of optimal frame completions of F0 obtained by appending a finite sequence of vectors with prescribed norms, where optimality is measured with respect to a general convex potential. In particular, our analysis includes the so-called Mean Square Error (MSE) and the Benedetto-Fickus’ frame potential. On a first step, we reduce the problem of finding the optimal completions to the computation of the minimum of a convex function in a convex compact polytope in R d . As a second step, we show that there exists a finite set (that can be explicitly computed in terms of a finite step algorithm that depends on F0 and the sequence of prescribed norms) such that the optimal frame completions with respect to a given convex potential can be described in terms of a distinguished element of this set. As a byproduct we characterize the cases of equality in Lidskii’s inequality from matrix theory.
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Materia
Frame Completions
Majorization
Lidskii'S Inequality
Schur-Horn Theorem
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:11336/33465
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/33465
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Optimal frame completionsMassey, Pedro GustavoRuiz, Mariano AndresStojanoff, DemetrioFrame CompletionsMajorizationLidskii'S InequalitySchur-Horn Theoremhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a finite sequence of vectors F0 in C d we describe the spectral and geometrical structure of optimal frame completions of F0 obtained by appending a finite sequence of vectors with prescribed norms, where optimality is measured with respect to a general convex potential. In particular, our analysis includes the so-called Mean Square Error (MSE) and the Benedetto-Fickus’ frame potential. On a first step, we reduce the problem of finding the optimal completions to the computation of the minimum of a convex function in a convex compact polytope in R d . As a second step, we show that there exists a finite set (that can be explicitly computed in terms of a finite step algorithm that depends on F0 and the sequence of prescribed norms) such that the optimal frame completions with respect to a given convex potential can be described in terms of a distinguished element of this set. As a byproduct we characterize the cases of equality in Lidskii’s inequality from matrix theory.Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaSpringer2014-12info: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/11336/33465Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Optimal frame completions; Springer; Advances In Computational Mathematics; 40; 5-6; 12-2014; 1011-10421019-7168CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10444-013-9339-7info:eu-repo/semantics/altIdentifier/doi/10.1007/s10444-013-9339-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-26T09:09:57Zoai:ri.conicet.gov.ar:11336/33465instacron: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 09:09:57.514CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimal frame completions
title Optimal frame completions
spellingShingle Optimal frame completions
Massey, Pedro Gustavo
Frame Completions
Majorization
Lidskii'S Inequality
Schur-Horn Theorem
title_short Optimal frame completions
title_full Optimal frame completions
title_fullStr Optimal frame completions
title_full_unstemmed Optimal frame completions
title_sort Optimal frame completions
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 Frame Completions
Majorization
Lidskii'S Inequality
Schur-Horn Theorem
topic Frame Completions
Majorization
Lidskii'S Inequality
Schur-Horn Theorem
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a finite sequence of vectors F0 in C d we describe the spectral and geometrical structure of optimal frame completions of F0 obtained by appending a finite sequence of vectors with prescribed norms, where optimality is measured with respect to a general convex potential. In particular, our analysis includes the so-called Mean Square Error (MSE) and the Benedetto-Fickus’ frame potential. On a first step, we reduce the problem of finding the optimal completions to the computation of the minimum of a convex function in a convex compact polytope in R d . As a second step, we show that there exists a finite set (that can be explicitly computed in terms of a finite step algorithm that depends on F0 and the sequence of prescribed norms) such that the optimal frame completions with respect to a given convex potential can be described in terms of a distinguished element of this set. As a byproduct we characterize the cases of equality in Lidskii’s inequality from matrix theory.
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
description Given a finite sequence of vectors F0 in C d we describe the spectral and geometrical structure of optimal frame completions of F0 obtained by appending a finite sequence of vectors with prescribed norms, where optimality is measured with respect to a general convex potential. In particular, our analysis includes the so-called Mean Square Error (MSE) and the Benedetto-Fickus’ frame potential. On a first step, we reduce the problem of finding the optimal completions to the computation of the minimum of a convex function in a convex compact polytope in R d . As a second step, we show that there exists a finite set (that can be explicitly computed in terms of a finite step algorithm that depends on F0 and the sequence of prescribed norms) such that the optimal frame completions with respect to a given convex potential can be described in terms of a distinguished element of this set. As a byproduct we characterize the cases of equality in Lidskii’s inequality from matrix theory.
publishDate 2014
dc.date.none.fl_str_mv 2014-12
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/11336/33465
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Optimal frame completions; Springer; Advances In Computational Mathematics; 40; 5-6; 12-2014; 1011-1042
1019-7168
CONICET Digital
CONICET
url http://hdl.handle.net/11336/33465
identifier_str_mv Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Optimal frame completions; Springer; Advances In Computational Mathematics; 40; 5-6; 12-2014; 1011-1042
1019-7168
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://link.springer.com/article/10.1007/s10444-013-9339-7
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10444-013-9339-7
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
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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