Rational Krylov for eigenvalue computation and model order reduction

Abstract

A rational Krylov algorithm for eigenvalue computation and model order reduction is described. It is shown how to implement it as a modified shift-and-invert spectral transformation Arnoldi decomposition. It is shown how to do deflation, locking converged eigenvalues and purging irrelevant approximations. Computing reduced order models of linear dynamical systems by moment matching of the transfer function is considered. Results are reported from one illustrative toy example and one practical example, a linear descriptor system from a computational fluid dynamics application.