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dc.contributor.author
Massey, Pedro Gustavo
dc.contributor.author
Ruiz, Mariano Andres
dc.contributor.author
Stojanoff, Demetrio
dc.date.available
2015-11-05T17:12:57Z
dc.date.issued
2015-03-15
dc.identifier.citation
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
dc.identifier.issn
0024-3795
dc.identifier.uri
http://hdl.handle.net/11336/2672
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier Science Inc.
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
CONVEX POTENTIALS
dc.subject
FRAMES
dc.subject
LIDSKII'S INEQUALITY
dc.subject
MAJORIZATION
dc.subject
PERTURBATION OF FRAMES
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Multiplicative Lidskii's inequalities and optimal perturbations of frames
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-03-30 10:35:44.97925-03
dc.journal.volume
469
dc.journal.pagination
539-568
dc.journal.pais
Países Bajos
dc.journal.ciudad
Amsterdam
dc.description.fil
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
dc.description.fil
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
dc.description.fil
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
dc.journal.title
Linear Algebra And Its Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://goo.gl/xNx2CJ
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1405.4277
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http//dx.doi.org/10.1016/j.laa.2014.12.004
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