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.

Multihomogeneous Polynomial Decomposition using Moment Matrices

BERNARDI, Alessandra;
2011-01-01

Abstract

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.
2011
International Symposium of Symbolic and Algebraic Computation
San Jose, CA, USA
June 2011
ISSAC 2011: PROCEEDINGS OF THE 36TH INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION
Leykin, A
35
42
9781450306751
http://www.issac-conference.org/2011/
Moment matrix, multihomogeneous polynomial decomposition, tensor decomposition; SYMMETRIC TENSORS, SECANT VARIETIES, SEGRE VARIETIES, SEPARATION, COMPLEXITY, RANK, MULTIPLICATION, IDENTIFICATION, PRINCIPLES, EXTENSION
BERNARDI A; BRACHAT J; COMON P; MOURRAIN B
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/129206
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