General Tensor Decomposition, Moment Matrices and Applications

Alessandra Bernardi; Jerome Brachat; Pierre Comon; Bernard Mourrain

doi:10.1016/j.jsc.2012.05.012

inria-00590965, version 3

General Tensor Decomposition, Moment Matrices and Applications

Alessandra Bernardi (, ) ¹, Jerome Brachat () ¹, Pierre Comon () ², Bernard Mourrain () ¹

Journal of Symbolic Computation 52, May (2013) 51-71

Résumé : The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated moment matrix problem and give a new criterion for flat extension of Quasi-Hankel matrices. We connect this criterion to the commutation characterisation of border bases. A new algorithm is described. It applies for general multihomogeneous tensors, extending the approach of J.J. Sylvester to binary forms. An example illustrates the algebraic operations involved in this approach and how the decomposition can be recovered from eigenvector computation.

1 : GALAAD (INRIA Sophia Antipolis)
INRIA – CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
2 : Grenoble Images Parole Signal Automatique (GIPSA-lab)
CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology

inria-00590965, version 3
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Contributeur : Bernard Mourrain <>
Soumis le : Jeudi 20 Octobre 2011, 20:52:07
Dernière modification le : Mardi 30 Juillet 2013, 13:16:13

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arXiv : 1105.1229

DOI : 10.1016/j.jsc.2012.05.012

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