Relative perturbation theory for hyperbolic eigenvalue problem

We give relative perturbation bounds for eigenvalues and perturbation bounds for eigenspaces of a hyperbolic eigenvalue problem Hx = lambda Jx, where H is a positive definite matrix and J is a diagonal matrix of signs. We consider two types of perturbations: when a graded matrix H=D*AD is perturbed in a graded sense to H+delta H= D*(A+delta A)D, and the multiplicative perturbations of the form H+delta H= (I + E)*H(I + E). Our bounds are simple to compute, compare well to the classical results, and can be used when analyzing numerical algorithms. (C) 2000 Elsevier Science Inc. All rights reserved.