Low rank approximation (LRA) of a matrix is a hot subject of modern
computations. In application to Big Data mining and analysis the input matrices
are usually so immense that one must apply superfast algorithms, which only
access a tiny fraction of the input entries and involve much fewer memory cells
and flops than an input matrix has entries. Recently we devised and analyzed
some superfast LRA algorithms; in this paper we extend a classical algorithm of
iterative refinement of the solution of linear systems of equations to
superfast refinement of a crude but reasonably close LRA; we also list some
heuristic recipes for superfast a posteriori estimation of the errors of LRA
and support our superfast refinement algorithm with some superfast heuristic
recipes for a posteriori error estimation of LRA and with superfast back and
forth transition between any LRA of a matrix and its SVD. Our algorithm of
iterative refinement of LRA is the first attempt of this kind and should
motivate further effort in that direction, but already our initial tests are in
good accordance with our formal study.Comment: 12.5 pages,, 1 table and 1 figur