Perturbation of eigenvalues for periodic matrix pairs via the Bauer–Fike theorems

In earlier papers, the Bauer–Fike technique was applied to the ordinary eigenvalue problem Ax=λx, the generalized eigenvalue problem Ax=λBx and the matrix polynomial eigenvalue problem ∑k=0mλkAkx=0. General multiple eigenvalues were dealt with and condition numbers were obtained for individual as well as clusters of eigenvalues. In this paper, we shall generalize the technique to the eigenvalue problem for regular periodic matrix pairs. Perturbation to eigenvalues, simple or multiple, finite or infinite, will be considered for perturbations of any size. For small perturbations, clusters of eigenvalues will be considered.