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

2009/06/01 by Vartan Choulakian, Choulakian, Vartan
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #Tensor decomposition and applications #Wireless Communication Networks Research

paper · pdf · doi:10.48550/arxiv.0906.0198

openalex publication_date 2009/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics

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