This talk will describe a method to compress a tensor by constructing
a piece-wise tensor approximation. This is constructed by partitioning
a tensor into sub-tensors and by constructing a low-rank tensor
approximation (in a given format) in each sub-tensor. Neither the
partition nor the ranks are fixed a priori, but, instead, they are
obtained in order to fulfill a prescribed accuracy and optimize the
storage. We also discuss a parallel algorithm that generates a
low-rank approximation of a distributed tensor using QR decomposition
with tournament pivoting. This algorithm can enable fast decisions
during the hierarchical compression procedure. Some numerical
experiments are proposed to illustrate the method.
This is joint work with M. Beaupere, V. Ehrlacher, D. Frenkiel,
D. Lombardi, and H. Song.
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