SOME NUMERICAL RESULTS ON THE RANK OF GENERIC THREE-WAY ARRAYS OVER R.

The aim of this paper is the introduction of a new method for the numerical computation of the rank of a three-way array X ∈ RI×J×K over R. We show that the rank of a three-way array over 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 Gr¨obner bases. Also, we show that for I = (K − 1)(J − 1) + 1 and 2 ≤ K ≤ J ≤ I, the rank for generic data has more than one rank value, and the minimum attained value is I. [ABSTRACT FROM AUTHOR]