Approximate solves in Krylov-based modeling methods

Rational Krylov methods are potentially one of the most robust and efficient algorithms to compute lower order approximations to linear time invariant dynamical systems that match a specified number of moments of the transfer function at multiple points in the complex plane. The characterization of multipoint rational interpolation in terms of bases of multiple Krylov spaces was developed recently. In this paper, we summarize some results concerning the use of approximate solutions to the linear systems of equations that arise on each step of the method. Such approximations are used to reduce the space and time required to produced the reduced order system.