On best rank one approximation of tensors

dc.contributor.authorFriedland, Shmuel
dc.contributor.authorMehrmann, Volker
dc.contributor.authorPajarola, Renato
dc.contributor.authorSuter, Susanne
dc.date.accessioned2021-12-17T10:10:38Z
dc.date.available2021-12-17T10:10:38Z
dc.date.issued2012-01-10
dc.description.abstractIn this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called 'alternating singular value decomposition'. This method is based on the computation of maximal singular values and the corresponding singular vectors of matrices. We also introduce a modification for this method and the alternating least squares method, which ensures that alternating iterations will always converge to a semi-maximal point. Finally, we introduce a new simple Newton-type method for speeding up the convergence of alternating methods near the optimum. We present several numerical examples that illustrate the computational performance of the new method in comparison to the alternating least square method.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15755
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14528
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.othersingular value decompositionen
dc.subject.otherrank one approximationen
dc.subject.otheralternating least squaresen
dc.subject.otherNewton's methoden
dc.titleOn best rank one approximation of tensorsen
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.issuenumber2012, 07en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200015A18 Eigenvalues, singular values, and eigenvectorsen
tub.subject.msc200015A69 Multilinear algebra, tensor productsen
tub.subject.msc200065D15 Algorithms for functional approximationen
tub.subject.msc200065H10 Systems of equationsen
tub.subject.msc200065K05 Mathematical programming methodsen
Files
Original bundle
Now showing 1 - 1 of 1
Loading…
Thumbnail Image
Name:
FriMPS11_ppt.pdf
Size:
468.54 KB
Format:
Adobe Portable Document Format
Description:
Collections