Refined methods for the identifiability of tensors |
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| Authors: | Cristiano Bocci Luca Chiantini Giorgio Ottaviani |
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| Affiliation: | 1. Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, Pian dei Mantellini 44, 53100, Siena, Italy
2. Dipartimento di Matematica e Informatica ‘Ulisse Dini’, Università di Firenze, Viale Morgagni 67/A, 50134, Florence, Italy
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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 (kle 0.9997frac{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 (kle 0.998frac{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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