Relative perturbation theory for hyperbolic singular value problem

We give relative perturbation bounds for singular values and perturbation bounds for singular subspaces of a hyperbolic singular value problem for the pair (G, J), where G is a full rank matrix and J is a diagonal matrix of signs. We consider two types of relative perturbations: G + deltaG = (B + deltaB)D and G + deltaG = (D) over bar((B) over bar + delta(B) over bar), depending whether G has full column or full row rank, respectively. In both cases we also consider relative element-wise perturbations of G which typically occur in numerical computations. (C) 2002 Elsevier Science Inc. All rights reserved.