Algebraic PGD for tensor separation and compression: an algorithmic approach

Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensionalboundary value problems(where many dimensions are associated with the space of parameters defining the problem). The PGD philosophy consists in providing a separated representation of the multidimensional solution using agreedy approachcombined with an alternated directions scheme to obtain the successive rank-one terms. This paper presents an algorithmic approach to high-dimensional tensorseparation based on solving theLeast Squares approximationin a separable format of multidimensional tensor using PGD. This strategy is usually embedded in a standard PGD code in order to compress the solution (reduce the number of terms and optimize the available storage capacity), but it stands also as an alternative and highly competitive method for tensor separation.