Mark Embree, Virginia Tech

Abstract

To compute a small subset of the eigenvalues of a matrix, contour integral algorithms evaluate the action of the resolvent on low-dimensional right and left subspaces, sampled at points on the contour.  These algorithms have grown in popularity over the past 15 years, and hold particular promise as potential black-box solvers for nonlinear eigenvalue problems.  We will describe this general class of methods, and show how they relate to system realization algorithms from control theory.  This observation motivates a new method for nonlinear eigenvalue problems based on rational interpolation in random tangential directions.  This talk describes joint work with Michael Brennan (MIT) and Serkan Gugercin (Virginia Tech).