Relative perturbation theory for strongly definitizable matrix pairs
Ivica Nakic
Abstract: We present a relative perturbation theory for strongly definitizable matrix pairs (H,K), i.e. for Hermitian matrix pairs which have separated positive and negative parts of the spectrum.
It is shown that, in some sense, this is the widest possible class of Hermitian matrix pairs for which such a theory can be obtained. This result generalizes the known result for the case when K is positive definite.
New eigenvalue perturbation estimates are also given for definite pairs. We hope that the new estimates will be useful in the analysis of numerical algorithms for eigenvalue computation.