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 Title Some numerical results on the rank of generic three-way arrays over $mathbbR$. Author(s) Vartan Choulakian Type Article in Journal Abstract The 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. ISSN 0895-4798; 1095-7162/e URL http://epubs.siam.org/doi/abs/10.1137/08073531X Language English Journal SIAM J. Matrix Anal. Appl. Volume 31 Number 4 Pages 1541--1551 Publisher Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA Year 2010 Edition 0 Translation No Refereed No
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