392 IGPM392.pdf        April 2014
TITLE Sampling Rules for Tensor Reconstruction in Hierarchical Tucker Format
AUTHORS Melanie Kluge
ABSTRACT 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