Calculation of linear bestL p -approximations

Abstract

In this paper we are concerned with finding theL p -solution (i.e. minimizing theL p -norm of the residual vector) to a linear approximation problem or, equivalenty, to an overdetermined system of linear equations. An embedding method is described in which the damped Newton iteration is applied to a series of “perturbed problems” in order to guarantee convergence and also increase the convergence rate.