A datasparse structure for representing functionrelated tensors with
a finite number of singularities is described. As it is well known,
singularities (or fast growth of the derivatives) can prevent the existence of
a lowrank approximation. A strategy for representing such a tensor
(matrix) in a datasparse form could be to approximate the blocks far from
singularities (admissible blocks) and continue hierarchically with the
nonadmissible blocks (e.g. Hmatrix technique). This will however lead to
a complicated structure if there are several singular points, and the
number of blocks will increase exponentially w.r.t. the dimension. We propose
to approximate not the admissible blocks but the whole tensor without the
nonadmissible ones. The approximation problem in this case goes beyond
the standard theory of linear algebra already for d=2. Some successful
algorithms and numerical examples from electronic structure calculations
are presented.
