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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 193, Issue 6, pp 1691–1702 | Cite as

Refined methods for the identifiability of tensors

  • Cristiano Bocci
  • Luca Chiantini
  • Giorgio Ottaviani
Article

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 \(k\le 0.9997\frac{2^n}{n+1}\) (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 \(k\le 0.998\frac{3^n}{2n+1}\) (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.

Keywords

Tensor decomposition Identifiability Secant variety 

Mathematics Subject Classification

14N05 15A69 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Cristiano Bocci
    • 1
  • Luca Chiantini
    • 1
  • Giorgio Ottaviani
    • 2
  1. 1.Dipartimento di Ingegneria dell’Informazione e Scienze MatematicheUniversità di SienaSienaItaly
  2. 2.Dipartimento di Matematica e Informatica ‘Ulisse Dini’Università di FirenzeFlorenceItaly

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