|Preprint-No.:||< 392 >||Published in:||April 2014||PDF-File:||IGPM392.pdf|
|Title:||Sampling Rules for Tensor Reconstruction in Hierarchical Tucker Format|
The subject of this article is the development of an algorithm that re- constructs a high-dimensional tensor by a hierarchical (H-) Tucker tensor with the help of a non-adaptive sampling rule. This sampling rule supports our approximation scheme coming from the matrix cross approximation and guarantees that we can build a tensor AH in the desired format from only a few entries of the original tensor A. Under mild assumptions AH is a reconstruction of A. In the numerical experiments we obtain convenient approximations also for tensors without low rank representation and for per- tubed tensors.
|Keywords:||tensor completion, tensor approximation, tensor train|