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

Superfast Approximate Linear Least Squares Solution of a Highly Overdetermined Linear System of Equations