Some Numerical Results on the Rank of Generic Three-Way Arrays over R

We introduce a new method for the numerical computation of the rank of a three-way array over R. We present some theoretical and numerical results based on the computation of Gröbner bases. Key words: Tensors; three-way arrays; Candecomp/Parafac; generic rank; typical rank; Segre variety; Veronese variety; Gröbner bases.