A Perturbation Method for Index Detection for Linear Matrix Pencils

Abstract

Rigorous, non-asymptotic bounds for the Puiseux expansion of the eigenvalue at infinity are given. Error analysis is provided. Further, the expected value of the eigenvector condition number of a randomly perturbed matrix is estimated. The latter result is applied to the Cayley transform of the linear pencil. Numerical simulations illustrating the theoretical findings are provided.