Measures of Scalability

dc.contributor.authorChen, Xuemei
dc.contributor.authorKutyniok, Gitta
dc.contributor.authorOkoudjou, Kasso
dc.contributor.authorPhilipp, Friedrich
dc.contributor.authorWang, Rongrong
dc.date.accessioned2021-12-17T10:12:05Z
dc.date.available2021-12-17T10:12:05Z
dc.date.issued2014-10-10
dc.description.abstractScalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For this, in this paper we introduce three novel quantitative measures of the closeness to scalability for frames in finite dimensional real Euclidean spaces. Besides the natural measure of scalability given by the distance of a frame to the set of scalable frames, another measure is obtained by optimizing a quadratic functional, while the third is given by the volume of the ellipsoid of minimal volume containing the symmetrized frame. After proving that these measures are equivalent in a certain sense, we establish bounds on the probability of a randomly selected frame to be scalable. In the process, we also derive new necessary and sufficient conditions for a frame to be scalable.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15803
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14576
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherconvex geometryen
dc.subject.otherquality measuresen
dc.subject.otherparseval frameen
dc.subject.otherscalable frameen
dc.titleMeasures of Scalabilityen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2014, 24en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200042C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansionsen

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