Refined methods for the identifiability of tensors
Algebraic Geometry
2013-05-14 v3
Abstract
We prove that the general tensor of size 2^n and rank k has a unique decomposition as the sum of decomposable tensors if k<= 0.9997 (2^n)/(n+1) (the constant 1 being the optimal value). Similarly, the general tensor of size 3^n and rank k has a unique decomposition as the sum of decomposable tensors if k<= 0.998 (3^n)/(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.
Keywords
Cite
@article{arxiv.1303.6915,
title = {Refined methods for the identifiability of tensors},
author = {Cristiano Bocci and Luca Chiantini and Giorgio Ottaviani},
journal= {arXiv preprint arXiv:1303.6915},
year = {2013}
}
Comments
12 pages, three Macaulay2 scripts as ancillary files. v3: final version to appear in Annali di Matematica Pura e Applicata