On the reduction of multivariate quadratic systems to best rank-1 approximation of three-way tensors

Alex P da Silva (1) , Pierre Comon (1) , André L F de Almeida (2)

1 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
2 GTEL - Wireless Telecom Research Group [Fortaleza]

In this paper, we show that a general quadratic multivariate system in the real field can be reduced to a best rank-1 three-way tensor approximation problem. This fact provides a new approach to tackle a system of quadratic polynomials equations. Some experiments using the standard alternating least squares (ALS) algorithm are drawn to evince the usefulness of rank-1 tensor approximation methods.

Mots clés: quadratic systems; tensor; rank-1 approximation

Domaines: Traitement du signal et de l'image [eess.SP]; Analyse numérique [math.NA]

Alex P da Silva, Pierre Comon, André L F de Almeida. On the reduction of multivariate quadratic systems to best rank-1 approximation of three-way tensors. Applied Mathematics Letters, 2016, 62, pp.9 - 15. ⟨10.1016/j.aml.2016.06.006⟩. ⟨hal-01567408⟩