Relative perturbation theory for hyperbolic singular value problem

AbstractWe 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+δG=(B+δB)D and G+δG=D̄(B̄+δB̄), 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