ИСТИНА

In this talk we survey recent essential developments [2, 3] of the ideas of low-rank matrix approximation proposed in [1] and consider their extensions to tensors. The practical impor- tance of the very approach consists in its paradigma of using only small part of matrix entries that allows one to construct a sufficiently accurate appoximation in a fast way for ”big data” matrices that cannot be placed in any available computer memory and are accessed implicitly through calls to a procedure producing any individual entry in demand. We consider how this approach can be used in the cases when we need to maintain nonnegativity of the elements.