TWO PERTURBATION BOUNDS FOR SINGULAR VALUES AND EIGENVALUES
The relative error in (alpha) over cap = alpha( 1 + delta) as an approximation to alpha is measured by delta = (alpha) over cap - alpha/alpha. In terms of this measurement we give a Hoffman-Wielandt type bound of singular values under additive perturbations and a Bauer-Fike type bound of eigenvalues under multiplicative perturbations.
perturbation bound singular value eigenvalue hoffman-wielandt bauer-fike