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Article: Necessary and sufficient conditions to perform Spectral Tetris

TitleNecessary and sufficient conditions to perform Spectral Tetris
Authors
Casazza, Peter G.Heinecke, AndreasKornelson, KeriWang, YangZhou, Zhengfang
KeywordsFrames
Majorization
Redundancy
Sparse matrices
Sparsity
Synthesis operator
Tight frames
Issue Date2013
Citation
Linear Algebra and Its Applications, 2013, v. 438, n. 5, p. 2239-2255 How to Cite?
DOI: http://dx.doi.org/10.1016/j.laa.2012.10.030
AbstractSpectral Tetris is a powerful tool for constructing sparse equal norm Hilbert space frames. We introduce a new form of Spectral Tetris which works for non-equal-norm frames. It is known that this method cannot construct all frames - even in the new case introduced here. Until now, it has been a mystery why Spectral Tetris sometimes works and sometimes fails. We provide a complete answer by giving necessary and sufficient conditions for Spectral Tetris to construct frames with prescribed vector norms and prescribed frame operator. We present a variety of examples and include cases where Spectral Tetris always works. © 2012 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/363719
ISSN
0024-3795
2023 Impact Factor: 1.0
2023 SCImago Journal Rankings: 0.837

 

DC FieldValueLanguage
dc.contributor.authorCasazza, Peter G.-
dc.contributor.authorHeinecke, Andreas-
dc.contributor.authorKornelson, Keri-
dc.contributor.authorWang, Yang-
dc.contributor.authorZhou, Zhengfang-
dc.date.accessioned2025-10-10T07:48:53Z-
dc.date.available2025-10-10T07:48:53Z-
dc.date.issued2013-
dc.identifier.citationLinear Algebra and Its Applications, 2013, v. 438, n. 5, p. 2239-2255-
dc.identifier.issn0024-3795-
dc.identifier.urihttp://hdl.handle.net/10722/363719-
dc.description.abstractSpectral Tetris is a powerful tool for constructing sparse equal norm Hilbert space frames. We introduce a new form of Spectral Tetris which works for non-equal-norm frames. It is known that this method cannot construct all frames - even in the new case introduced here. Until now, it has been a mystery why Spectral Tetris sometimes works and sometimes fails. We provide a complete answer by giving necessary and sufficient conditions for Spectral Tetris to construct frames with prescribed vector norms and prescribed frame operator. We present a variety of examples and include cases where Spectral Tetris always works. © 2012 Elsevier Inc. All rights reserved.-
dc.languageeng-
dc.relation.ispartofLinear Algebra and Its Applications-
dc.subjectFrames-
dc.subjectMajorization-
dc.subjectRedundancy-
dc.subjectSparse matrices-
dc.subjectSparsity-
dc.subjectSynthesis operator-
dc.subjectTight frames-
dc.titleNecessary and sufficient conditions to perform Spectral Tetris-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.laa.2012.10.030-
dc.identifier.scopuseid_2-s2.0-84872111695-
dc.identifier.volume438-
dc.identifier.issue5-
dc.identifier.spage2239-
dc.identifier.epage2255-

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