Refined methods for the identifiability of tensors
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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