In the paper, we address the important problem of tensor decompositions which can be seen as a generalisation of Singular Value Decomposition for 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 which applies for general multihomogeneous tensors, extending the approach of J.J. Sylvester on binary forms. An example illustrates the algebraic operations involved in this approach and how the decomposition can be recovered from eigenvector computation.
General tensor decomposition, moment matrices and applications / Bernardi, Alessandra; Jerome, Brachat; Pierre, Comon; Bernard, Mourrain. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 52(2013), pp. 51-71. [10.1016/j.jsc.2012.05.012]
Titolo: | General tensor decomposition, moment matrices and applications | |
Autori: | Bernardi, Alessandra; Jerome, Brachat; Pierre, Comon; Bernard, Mourrain | |
Autori Unitn: | ||
Titolo del periodico: | JOURNAL OF SYMBOLIC COMPUTATION | |
Anno di pubblicazione: | 2013 | |
Codice identificativo Scopus: | 2-s2.0-84873569701 | |
Codice identificativo Pubmed: | 10.1016/j.jsc.2012.05.012 | |
Codice identificativo WOS: | WOS:000316648400005 | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jsc.2012.05.012 | |
Handle: | http://hdl.handle.net/11572/134905 | |
Citazione: | General tensor decomposition, moment matrices and applications / Bernardi, Alessandra; Jerome, Brachat; Pierre, Comon; Bernard, Mourrain. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 52(2013), pp. 51-71. [10.1016/j.jsc.2012.05.012] | |
Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |
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