Contour Integral Methods for Nonlinear Eigenvalue Problems: A Systems Theory Perspective
Contour integral methods for nonlinear eigenvalue problems seek to compute a subset of the spectrum in a bounded region of the complex plane. We briefly survey this class of algorithms, establishing a relationship to system realization techniques in control theory. This connection motivates new contour integral methods that build on recent developments in rational interpolation of dynamical systems. The resulting techniques, which replace the usual Hankel matrices with Loewner matrix pencils, incorporate general interpolation schemes and permit ready recovery of eigenvectors. Numerical examples illustrate the potential of this approach.
This talk describes joint work with Michael Brennan (MIT) and Serkan Gugercin (Virginia Tech).