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

Abstract

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.