Constrained Tensor Product Approximations based on Penalized Best Approximations

Anthony Nouy (1) , Antonio Falco (2)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 CEU-UCH - Universidad Cardenal Herrera-CEU

In this paper, we propose some alternative definitions of tensor product approximations based on the progressive construction of successive best rank-one approximations, with eventual updates of previously computed elements. In particular, it can be interpreted as a constrained multidimensional singular value decomposition where the constraints are imposed by means a penalty method. A convergence proof of these decompositions is established under some general assumptions on the penalty functional. Heuristic alternated direction algorithms are provided, also definitions and algorithms are detailed for an application of interest consisting in imposing bounds on each tensor component.

Mots clés: Tensor product approximation; Constrained Separated Representation; Penalization; Convex optimization; Constrained Singular Value decomposition; Proper Generalized Decomposition

Domaines: Analyse numérique [math.NA]

Anthony Nouy, Antonio Falco. Constrained Tensor Product Approximations based on Penalized Best Approximations. 2011. ⟨hal-00577942⟩