Relative perturbation theory for hyperbolic eigenvalue problem Original Research Article

We give relative perturbation bounds for eigenvalues and perturbation bounds for eigenspaces of a hyperbolic eigenvalue problem Hx=λJx, 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+δH=D*(A+δA)D, and the multiplicative perturbations of the form H+δH=(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.