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).
Bocci, C., Chiantini, L., Ottaviani, G. (2014). Refined methods for the identifiability of tensors. ANNALI DI MATEMATICA PURA ED APPLICATA, 193, 1691-1702 [10.1007/s10231-013-0352-8].
Refined methods for the identifiability of tensors
BOCCI, CRISTIANO;CHIANTINI, LUCA;
2014-01-01
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).
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https://hdl.handle.net/11365/48302
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