ИСТИНА

The construction of most successful numerical algorithms for multi-dimensional problems usually involves multi-index arrays, also called tensors, and capitalizes on those tensor decompositions that reduce, one way or another, to low-rank matrices associated with the given tensors. It can be argued that the most of recent progress is due to the TT and HT decompostions. The differences between the two decompositions may look as rather subtle, because the both are based on the same dimensionality reduction tree and exploit seemingly the same idea. In this talk, we analyze the differences between the two decompositions and present them in a clear and simple way. Besides that, we demostrate some new applciations of tensor approximations in numerical analysis.