Error analysis for a matrix pencil of Hankel matrices with perturbed complex moments

Abstract

In this paper, we present perturbation results for eigenvalues of a matrix pencil of Hankel matrices for which the elements are given by complex moments. These results are extended to the case that matrices have a block Hankel structure. The influence of quadrature error on eigenvalues that lie inside a given integral path can be reduced by using Hankel matrices of an appropriate size. These results are useful for discussing the numerical behavior of root finding methods and eigenvalue solvers which make use of contour integrals. Results from some numerical experiments are consistent with the theoretical results.