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General Tensor Decomposition, Moment Matrices and Applications

Alessandra Bernardi 1 Jerome Brachat 1 Pierre Comon 2 Bernard Mourrain 1 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : 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.
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Submitted on : Thursday, October 20, 2011 - 8:52:07 PM
Last modification on : Thursday, August 4, 2022 - 4:52:38 PM
Long-term archiving on: : Saturday, January 21, 2012 - 2:35:59 AM


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Alessandra Bernardi, Jerome Brachat, Pierre Comon, Bernard Mourrain. General Tensor Decomposition, Moment Matrices and Applications. Journal of Symbolic Computation, 2013, 52 (May), pp.51-71. ⟨10.1016/j.jsc.2012.05.012⟩. ⟨inria-00590965v3⟩



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