engleski

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+\delta G= (B+\delta B)D and G+\delta G=\bar D(\bar B+\bar \delta B), 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.

hyperbolic singular value problems ; perturbation theory

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