Some Numerical Results on the Rank of Generic Three-Way Arrays over R
Vartan Choulakian
TL;DR
This paper introduces a new numerical method for determining the rank of three-way arrays over the real numbers, leveraging polynomial systems and Grobner bases to obtain concrete results.
Contribution
It presents a novel approach connecting tensor rank computation to solving polynomial equations using Grobner bases, providing new numerical insights.
Findings
Numerical results on the rank of three-way arrays over R.
Relationship between array rank and solution sets of polynomial systems.
Application of Grobner bases to tensor rank computation.
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.
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Taxonomy
TopicsTensor decomposition and applications · Wireless Communication Networks Research · Advanced Wireless Communication Techniques