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TitleGeneral tensor decomposition, moment matrices and applications
Author(s) A. Bernardi, J. Brachat, P. Comon, Bernard Mourrain
TypeArticle in Journal
AbstractThe 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.
KeywordsTensor, Decomposition, Multihomogeneous polynomial, Rank, Hankel operator, Moment matrix, Flat extension
URL http://www.sciencedirect.com/science/article/pii/S0747717112001290
JournalJournal of Symbolic Computation
Pages51 - 71
NoteInternational Symposium on Symbolic and Algebraic Computation
Translation No
Refereed No