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arXiv · 1303.6915

Refined methods for the identifiability of tensors

Cristiano Bocci·Luca Chiantini·Giorgio Ottaviani
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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.

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Cristiano Bocci, Luca Chiantini, Giorgio Ottaviani. 2013-05-13. Refined methods for the identifiability of tensors. https://arxiv.org/abs/1303.6915

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