Approximation by Partial Isometries and Symmetric Approximation of Finite Frames

Autores
Antezana, Jorge Abel; Chiumiento, Eduardo Hernan
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.
Fil: Antezana, Jorge Abel. 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: Chiumiento, Eduardo Hernan. 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
Finite Frame
Lowdin Orthogonalization
Partial Isometry
Polar Decomposition
Singular Value Decomposition
Symmetric Approximation
Unitarily Invariant Norms
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:11336/39422
Acceder
id CONICETDig_94629730c38b2b20536075439d4aedc7
oai_identifier_str oai:ri.conicet.gov.ar:11336/39422
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Approximation by Partial Isometries and Symmetric Approximation of Finite FramesAntezana, Jorge AbelChiumiento, Eduardo HernanFinite FrameLowdin OrthogonalizationPartial IsometryPolar DecompositionSingular Value DecompositionSymmetric ApproximationUnitarily Invariant Normshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.Fil: Antezana, Jorge Abel. 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: Chiumiento, Eduardo Hernan. 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; ArgentinaBirkhauser Boston Inc2017-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/39422Antezana, Jorge Abel; Chiumiento, Eduardo Hernan; Approximation by Partial Isometries and Symmetric Approximation of Finite Frames; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 5-2017; 1-211069-5869CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-017-9547-5info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00041-017-9547-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:22:19Zoai:ri.conicet.gov.ar:11336/39422instacron: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 13:22:19.934CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
spellingShingle Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
Antezana, Jorge Abel
Finite Frame
Lowdin Orthogonalization
Partial Isometry
Polar Decomposition
Singular Value Decomposition
Symmetric Approximation
Unitarily Invariant Norms
title_short Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_full Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_fullStr Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_full_unstemmed Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_sort Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
dc.creator.none.fl_str_mv Antezana, Jorge Abel
Chiumiento, Eduardo Hernan
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Chiumiento, Eduardo Hernan
author_role author
author2 Chiumiento, Eduardo Hernan
author2_role author
dc.subject.none.fl_str_mv Finite Frame
Lowdin Orthogonalization
Partial Isometry
Polar Decomposition
Singular Value Decomposition
Symmetric Approximation
Unitarily Invariant Norms
topic Finite Frame
Lowdin Orthogonalization
Partial Isometry
Polar Decomposition
Singular Value Decomposition
Symmetric Approximation
Unitarily Invariant Norms
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.
Fil: Antezana, Jorge Abel. 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: Chiumiento, Eduardo Hernan. 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 We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.
publishDate 2017
dc.date.none.fl_str_mv 2017-05
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/11336/39422
Antezana, Jorge Abel; Chiumiento, Eduardo Hernan; Approximation by Partial Isometries and Symmetric Approximation of Finite Frames; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 5-2017; 1-21
1069-5869
CONICET Digital
CONICET
url http://hdl.handle.net/11336/39422
identifier_str_mv Antezana, Jorge Abel; Chiumiento, Eduardo Hernan; Approximation by Partial Isometries and Symmetric Approximation of Finite Frames; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 5-2017; 1-21
1069-5869
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-017-9547-5
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00041-017-9547-5
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
dc.publisher.none.fl_str_mv Birkhauser Boston Inc
publisher.none.fl_str_mv Birkhauser Boston 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
_version_ 1842981229154009088
score 12.48226

Publicaciones similares