Seminars

The Conditioning of the Generalized Hankel Eigenvalue Problem

George Labahn, University of Waterloo, Canada.


The generalized Hankel eigenvalue problem $H_1 y = \lambda H y$, where $H$ is a Hankel matrix and $H_1$ is a shift of $H$ appears in a number of important applications, in particular the reconstruction of the shape of a polygon from its moments, and the sparse multivariate interpolation problem for black box polynomials. In this talk we discuss the situation where the input data are only known up to a certain precision. We show that the sensitivity of both structured and unstructured perturbations are (rather surprisingly) measured by essentially the same quantity. In addition we give a lower bound for the most sensitive eigenvalue of the generalized Hankel eigenvalue problem which requires us the study of condition number of certain scaled Vandermonde matrices. The analysis shows that this sensitivity grows exponentially with the size of our matrix.