On the solution of the linear least squares problems and pseudo-inverses

It is known that the computed least squares solution x of Ax=b, in the presence of the round-off error, satisfies the perturbed equation (A+E)(x+h)=b+f. The practical considerations of computing the solution are discussed and it is found that rank (A+E)=rank (A). A general analysis of the condition of the linear least squares problems and pseudo-inverses is then presented using this assumption. Norms of relevant round-off error perturbations are estimated for two known methods of solution. Comparison between different algorithms is given by numerical examples.Peer reviewed: YesNRC publication: Ye