  The aim of this paper is the introduction of a new method for the numerical
computation of the rank of a three-way array. 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 Grobner bases.
  Key words: Tensors; three-way arrays; Candecomp/Parafac; Indscal; generic
rank; typical rank; Veronese variety; Segre variety; Grobner bases.
  AMS classification: Primary 15A69; Secondary 15A72, 15A18.
