Section: New Results

Tensor approximation and HPC

Participant : Damiano Lombardi.

In [26] a hierarchical adaptive piece-wise tensor decomposition is proposed to approximate high-dimensional functions. Neither the subtensor partitioning nor the rank of the approximation in each of the partitions are fixed a priori. Instead, they are computed to fulfill a prescribed accuracy. Two main contributions are proposed. A greedy error distribution scheme, that allows to adaptively construct the approximation in each of the partitions and a hierarchical tree algorithm that optimise the subtensor partitioning to minimise the storage. Several example on challenging functions are proposed.