Some Numerical Results on the Rank of Generic Three-Way Arrays over R
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. 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.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.