Refined methods for the identifiability of tensors

2013/03/27 by Cristiano Bocci, Bocci, Cristiano, Luca Chiantini +3 · 1 citation
Mathematics · #14N05 #15A69 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14N05 #msc:15A69

paper · pdf · doi:10.48550/arxiv.1303.6915

12 pages, three Macaulay2 scripts as ancillary files. v3: final version to appear in Annali di Matematica Pura e Applicata

arxiv created 2013/05/13 · arxiv updated 2013/05/14

Abstract

We prove that the general tensor of size 2ⁿ and rank k has a unique decomposition as the sum of decomposable tensors if k<= 0.9997 (2ⁿ)/(n+1) (the constant 1 being the optimal value). Similarly, the general tensor of size 3ⁿ and rank k has a unique decomposition as the sum of decomposable tensors if k<= 0.998 (3ⁿ)/(2n+1) (the constant 1 being the optimal value). Some results of this flavor are obtained for tensors of any size, but the explicit bounds obtained are weaker.

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