A fast Kaczmarz-like solver for linear least squares problems

In this paper we present a "mixture" between a classical Kaczmarz's algorit hm with relaxation parameter and an approximate orthogonalization procedure dye to Z. Kovarik. We prove that the sequence of approximations generated by the new algorithm so obtained converges, in the case of consistent least squares problems, to a solution (for values of the relaxation parameter in the interval (0, 2)). The numerical experiments described at the end of th e paper on a discretization of a (model) first kind Fredholm integral equat ion, show the fact that the convergence properties of our algorithm are ind ependent on the dimensions of the discretization matrix and can be improved by an apropriate choice of the relaxation parameter.