Perturbation theory for orthogonal projection methods with applications to least squares and total least squares (Q1908189)

The paper presents new perturbation theory for orthogonal projection methods with applications to least squares (LS) and total least squares (TLS). Current perturbation theory does not justify the superiority of TLS over LS. The authors derive new lower and upper perturbation bounds for orthogonal projection methods in terms of the subspace angle and the norms of the solutions. These bounds show that TLS is usually more robust than LS under perturbation of all the data. Furthermore, the new bounds permit a comparison between the LS and TLS solutions as well as between any two orthogonal projection methods. Numerical simulations show that the lower and upper bounds provide realistic estimates of the error. They illustrate that the TLS subspaces usually ``filter'' more noise that the LS subspaces.