Generalized frame operator distance problems

Autores
Massey, Pedro Gustavo; Rios, Noelia Belén; Stojanoff, Demetrio
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let S∈Md(C)+ be a positive semidefinite d×d complex matrix and let a=(ai)i∈Ik ∈R>0 k, indexed by Ik={1,...,k}, be a k-tuple of positive numbers. Let Td(a) denote the set of families G={gi}i∈Ik ∈(Cd)k such that ‖gi‖2=ai, for i∈Ik; thus, Td(a) is the product of spheres in Cd endowed with the product metric. For a strictly convex unitarily invariant norm N in Md(C), we consider the generalized frame operator distance function Θ(N,S,a) defined on Td(a), given by Θ(N,S,a)(G)=N(S−SG) where SG=∑_{i∈Ik} gigi^⁎ ∈ Md(C)+. In this paper we determine the geometrical and spectral structure of local minimizers G0∈Td(a) of Θ(N,S,a). In particular, we show that local minimizers are global minimizers, and that these families do not depend on the particular choice of N.
Fil: Massey, Pedro Gustavo. 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
Fil: Rios, Noelia Belén. 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
Fil: Stojanoff, Demetrio. 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
Materia
MATRIX APPROXIMATION
UNITARILY INVARIANT NORMS
MAJORIZATION
FRAME OPERATOR DISTANCE
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:11336/106610
Acceder
id CONICETDig_865acb4ab0075b375cde496f0ce227e8
oai_identifier_str oai:ri.conicet.gov.ar:11336/106610
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Generalized frame operator distance problemsMassey, Pedro GustavoRios, Noelia BelénStojanoff, DemetrioMATRIX APPROXIMATIONUNITARILY INVARIANT NORMSMAJORIZATIONFRAME OPERATOR DISTANCEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let S∈Md(C)+ be a positive semidefinite d×d complex matrix and let a=(ai)i∈Ik ∈R>0 k, indexed by Ik={1,...,k}, be a k-tuple of positive numbers. Let Td(a) denote the set of families G={gi}i∈Ik ∈(Cd)k such that ‖gi‖2=ai, for i∈Ik; thus, Td(a) is the product of spheres in Cd endowed with the product metric. For a strictly convex unitarily invariant norm N in Md(C), we consider the generalized frame operator distance function Θ(N,S,a) defined on Td(a), given by Θ(N,S,a)(G)=N(S−SG) where SG=∑_{i∈Ik} gigi^⁎ ∈ Md(C)+. In this paper we determine the geometrical and spectral structure of local minimizers G0∈Td(a) of Θ(N,S,a). In particular, we show that local minimizers are global minimizers, and that these families do not depend on the particular choice of N.Fil: Massey, Pedro Gustavo. 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; ArgentinaFil: Rios, Noelia Belén. 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; ArgentinaFil: Stojanoff, Demetrio. 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; ArgentinaAcademic Press Inc Elsevier Science2019-11info: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/11336/106610Massey, Pedro Gustavo; Rios, Noelia Belén; Stojanoff, Demetrio; Generalized frame operator distance problems; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 479; 2; 11-2019; 1738-17630022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022247X19305827info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2019.07.021info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1812.10365info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:11:17Zoai:ri.conicet.gov.ar:11336/106610instacron: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:34982025-09-10 13:11:18.195CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Generalized frame operator distance problems
title Generalized frame operator distance problems
spellingShingle Generalized frame operator distance problems
Massey, Pedro Gustavo
MATRIX APPROXIMATION
UNITARILY INVARIANT NORMS
MAJORIZATION
FRAME OPERATOR DISTANCE
title_short Generalized frame operator distance problems
title_full Generalized frame operator distance problems
title_fullStr Generalized frame operator distance problems
title_full_unstemmed Generalized frame operator distance problems
title_sort Generalized frame operator distance problems
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
author_role author
author2 Rios, Noelia Belén
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv MATRIX APPROXIMATION
UNITARILY INVARIANT NORMS
MAJORIZATION
FRAME OPERATOR DISTANCE
topic MATRIX APPROXIMATION
UNITARILY INVARIANT NORMS
MAJORIZATION
FRAME OPERATOR DISTANCE
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 S∈Md(C)+ be a positive semidefinite d×d complex matrix and let a=(ai)i∈Ik ∈R>0 k, indexed by Ik={1,...,k}, be a k-tuple of positive numbers. Let Td(a) denote the set of families G={gi}i∈Ik ∈(Cd)k such that ‖gi‖2=ai, for i∈Ik; thus, Td(a) is the product of spheres in Cd endowed with the product metric. For a strictly convex unitarily invariant norm N in Md(C), we consider the generalized frame operator distance function Θ(N,S,a) defined on Td(a), given by Θ(N,S,a)(G)=N(S−SG) where SG=∑_{i∈Ik} gigi^⁎ ∈ Md(C)+. In this paper we determine the geometrical and spectral structure of local minimizers G0∈Td(a) of Θ(N,S,a). In particular, we show that local minimizers are global minimizers, and that these families do not depend on the particular choice of N.
Fil: Massey, Pedro Gustavo. 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
Fil: Rios, Noelia Belén. 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
Fil: Stojanoff, Demetrio. 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
description Let S∈Md(C)+ be a positive semidefinite d×d complex matrix and let a=(ai)i∈Ik ∈R>0 k, indexed by Ik={1,...,k}, be a k-tuple of positive numbers. Let Td(a) denote the set of families G={gi}i∈Ik ∈(Cd)k such that ‖gi‖2=ai, for i∈Ik; thus, Td(a) is the product of spheres in Cd endowed with the product metric. For a strictly convex unitarily invariant norm N in Md(C), we consider the generalized frame operator distance function Θ(N,S,a) defined on Td(a), given by Θ(N,S,a)(G)=N(S−SG) where SG=∑_{i∈Ik} gigi^⁎ ∈ Md(C)+. In this paper we determine the geometrical and spectral structure of local minimizers G0∈Td(a) of Θ(N,S,a). In particular, we show that local minimizers are global minimizers, and that these families do not depend on the particular choice of N.
publishDate 2019
dc.date.none.fl_str_mv 2019-11
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/11336/106610
Massey, Pedro Gustavo; Rios, Noelia Belén; Stojanoff, Demetrio; Generalized frame operator distance problems; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 479; 2; 11-2019; 1738-1763
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/106610
identifier_str_mv Massey, Pedro Gustavo; Rios, Noelia Belén; Stojanoff, Demetrio; Generalized frame operator distance problems; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 479; 2; 11-2019; 1738-1763
0022-247X
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/abs/pii/S0022247X19305827
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2019.07.021
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1812.10365
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 Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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
_version_ 1842980577484996608
score 12.993085

Publicaciones similares