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Preprint (Vorabdruck) zugänglich unter
URN: urn:nbn:de:bsz:291-scidok-43919
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4391/


The three-way decomposition

Ibraghimov, Ilghiz

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Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universit├Ąt des Saarlandes
Bandnummer: 66
Sprache: Englisch
Erstellungsjahr: 2002
Publikationsdatum: 02.12.2011
Kurzfassung auf Englisch: In this article we discuss the decomposition of A_{k}\in\mathbb{R}^{n_{1}\times n_{2}},k=1,...,n_{3} as A_{k}\simeq BE\hat{D}_{k}C^{*} in the Frobenius norm, where B\in\mathbb{R}^{n_{1}\times r} and C\in\mathbb{R}^{n_{2}\times r} have normalized columns, E and \hat{D}_{k}\in\mathbb{R}^{r\times r} are diagonal and \overset{n_{3}}{\sum}\hat{D}_{k}^{2} is the identity matrix. This decomposition is widely used in the data processing and is the generalization of the singular value decomposition for the 3 dimensional case. We propose a new algorithm for finding B, C, \hat{D}_{k} and E if A_{k} and r are given and B, C have full column rank. If A_{k} have exact decomposition then this algorithm has a linear convergence. An implementation of the numerical algorithm was developed, several examples were tested and good results obtained.
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