General tensor decomposition, moment matrices and applications

Authors:
A. Bernardi;J. Brachat;P. Comon;B. Mourrain
Affiliations:
GALAAD, INRIA Méditerranée, Sophia-Antipolis, France;GALAAD, INRIA Méditerranée, Sophia-Antipolis, France;GIPSA-Lab, Grenoble campus BP. 46, 38402 St Martin dHeres cedex, France;GALAAD, INRIA Méditerranée, Sophia-Antipolis, France
Venue:
Journal of Symbolic Computation
Year:
2013

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Abstract

The tensor decomposition addressed in this paper may be seen as a generalization 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 characterization of border bases. A new algorithm is described. It applies for general multihomogeneous tensors, extending the approach on binary forms by J.J. Sylvester. An example illustrates the algebraic operations involved in this approach and how the decomposition can be recovered from eigenvector computation.