Fast randomized linear least squares

Least squares approximation is a technique for finding an approximate solution to a system of linear equations that has no exact solution. In this paper, we are concerned with fast randomized approximation of Linear Least Squares (LLS) problems. Two algorithms are presented and compared: the first employing the combination of count-sketch with Subsampled Randomized Hadamard transform and in the second we combine count-sketch with a Gaussian projection. Both algorithms make use of QR factorization. The condition number of randomized LLS is computed. Finally, an application in space geodesy is presented for computing the geopotential harmonic coefficients with the aim of computing the gravitational potential.