Optimal frame completions

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 ana...

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Detalles Bibliográficos
Autores principales: Massey, Pedro Gustavo, Ruiz, Mariano Andrés, Stojanoff, Demetrio
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2014
Materias:
Matemática
Frame completions
Majorization
Lidskii's inequality
Schur-Horn theorem
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/98319
https://ri.conicet.gov.ar/11336/33465
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-98319
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Frame completions
Majorization
Lidskii's inequality
Schur-Horn theorem
spellingShingle Matemática
Frame completions
Majorization
Lidskii's inequality
Schur-Horn theorem
Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Stojanoff, Demetrio
Optimal frame completions
topic_facet Matemática
Frame completions
Majorization
Lidskii's inequality
Schur-Horn theorem
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.
format Articulo
Preprint
author Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Stojanoff, Demetrio
author_facet Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Stojanoff, Demetrio
author_sort Massey, Pedro Gustavo
title Optimal frame completions
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
publishDate 2014
url http://sedici.unlp.edu.ar/handle/10915/98319
https://ri.conicet.gov.ar/11336/33465
work_keys_str_mv AT masseypedrogustavo optimalframecompletions
AT ruizmarianoandres optimalframecompletions
AT stojanoffdemetrio optimalframecompletions
bdutipo_str Repositorios
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