Table of Contents
ISRN Geometry
Volume 2013 (2013), Article ID 241835, 3 pages
http://dx.doi.org/10.1155/2013/241835
Research Article

An Upper Bound for the Tensor Rank

Department of Mathematics, University of Trento, 38123 Povo, Italy

Received 18 April 2013; Accepted 12 May 2013

Academic Editors: J. L. Cieśliński, J. Montaldi, and J. Porti

Copyright © 2013 E. Ballico. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. H. Lim and V. de Silva, “Tensor rank and the ill-posedness of the best low-rank approximation problem,” SIAM Journal on Matrix Analysis and Applications, vol. 30, no. 3, pp. 1084–1127, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. Comon, “Tensor decompositions: state of the art and applications,” in Mathematics in Signal Processing, V (Coventry, 2000), vol. 71 of Institute of Mathematics and its Applications Conference Series, New Series, pp. 1–24, Oxford University Press, Oxford, UK, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. T. G. Kolda and B. W. Bader, “Tensor decompositions and applications,” SIAM Review, vol. 51, no. 3, pp. 455–500, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. M. Landsberg, Tensors: Geometry and Applications, vol. 128 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 2012. View at MathSciNet
  5. L. H. Lim and P. Comon, “Multiarray signal processing: tensor decomposition meets compressed sensing,” Comptes Rendus Mecanique, vol. 338, pp. 311–320, 2010. View at Google Scholar
  6. E. Ballico, “An upper bound for the symmetric tensor rank of a polynomial in a large number of variables,” Geometry, vol. 2013, Article ID 715907, p. 2, 2013. View at Publisher · View at Google Scholar
  7. V. Strassen, “Rank and optimal computation of generic tensors,” Linear Algebra and Its Applications, vol. 52-53, pp. 645–685, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Bocci, L. Chiantini, and G. Ottaviani, “Refined methods for the identifiability of tensors,” Annali di Matematica Pura e Applicata, http://arxiv.org/abs/1303.6915.
  9. A. Białynicki-Birula and A. Schinzel, “Representations of multivariate polynomials by sums of univariate polynomials in linear forms,” Colloquium Mathematicum, vol. 112, no. 2, pp. 201–233, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. Białynicki-Birula and A. Schinzel, “Corrigendum to “representatons of multivariate polynomials by sums of univariate polynomials in linear forms” (Colloq. Math. 112 (2008), 201–233) [MR2383331],” Colloquium Mathematicum, vol. 125, no. 1, p. 139, 2011. View at Publisher · View at Google Scholar · View at MathSciNet