Effective identifiability criteria for tensors and polynomials

Alex Massarenti; Massimiliano Mella; Giovanni Staglianò

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arXiv · 1703.02637

Effective identifiability criteria for tensors and polynomials

Alex Massarenti·Massimiliano Mella·Giovanni Staglianò

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Abstract

A tensor $T$, in a given tensor space, is said to be $h$-identifiable if it admits a unique decomposition as a sum of $h$ rank one tensors. A criterion for $h$-identifiability is called effective if it is satisfied in a dense, open subset of the set of rank $h$ tensors. In this paper we give effective $h$-identifiability criteria for a large class of tensors. We then improve these criteria for some symmetric tensors. For instance, this allows us to give a complete set of effective identifiability criteria for ternary quintic polynomial. Finally, we implement our identifiability algorithms in Macaulay2.

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BibTeX RIS

Alex Massarenti, Massimiliano Mella, Giovanni Staglianò. 2017-03-07. Effective identifiability criteria for tensors and polynomials. https://arxiv.org/abs/1703.02637

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