ИСТИНА

In this talk we survey recent essential developments [2, 3] of the ideas of low-rank matrix approximation proposed in [1]. The practical importance 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. During the two recent decades the approach has become a powerful numerical instrument in a tremendous variety of applications. However, its theoretical grounds still invite the researchers to provide them a better look. We discuss the notable new findings and as well some perspectives and open questions.