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TitleSome numerical results on the rank of generic three-way arrays over $mathbbR$.
Author(s) Vartan Choulakian
TypeArticle in Journal
AbstractThe aim of this paper is the introduction of a new method for the numerical computation of the rank of a three-way array $\mathbf{X}\in\mathbb{R}^{I\times J\times K}$ over $\mathbb{R}$. We show that the rank of a three-way array over $\mathbb{R}$ is intimately related to the real solution set of a system of polynomial equations. Using this, we present some numerical results based on the computation of Gröbner bases. Also, we show that for $I=(K-1)(J-1)+1$ and $2\leq K\leq J\leq I$, the rank for generic data has more than one rank value, and the minimum attained value is I.

ISSN0895-4798; 1095-7162/e
URL http://epubs.siam.org/doi/abs/10.1137/08073531X
LanguageEnglish
JournalSIAM J. Matrix Anal. Appl.
Volume31
Number4
Pages1541--1551
PublisherSociety for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
Year2010
Edition0
Translation No
Refereed No
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