Relative perturbation theory for definite matrix pairs and hyperbolic eigenvalue problem

摘要: In this paper, new relative perturbation bounds for the eigenvalues as well eigensubspaces are developed definite Hermitian matrix pairs and quadratic hyperbolic eigenvalue problem. First, we derive sin ? type theorems of ( A , B ) where both C m × nonsingular matrices with particular emphasis, is a diagonal ?1. Further, consider following problem µ 2 M + K v = 0 n given matrices. Using proper linearization develop corresponding considered The uniform depend only on M, C, K, perturbations ?M, ?C ?K standard gaps. quality illustrated through numerical examples.