  With a high probability the Sarlos randomized algorithm of 2006 outputs a
nearly optimal least squares solution of a highly overdeterminedlinear system
of equations. We propose its simple deterministic variation which computes such
a solution for a random input whp and therefore computes it deterministically
for a large input class. Unlike the Sarlos original algorithm our variation
performs computations at sublinear cost or, as we say, superfast, that is, by
using much fewer memory cells and arithmetic operations than an input matrix
has entries. Our extensive tests are in good accordance with this result.
