Pade approximations of large-scale dynamic systems with Lanczos methods

The utility of Lanczos methods for the approximation of large-scale dynamical systems is considered. In particular, it is shown that the Lanczos method is a technique for yielding Pad'e approximants which has several advantages over more traditional explicit moment matching approaches. An extension of the Lanczos algorithm is developed for computing multi-point Pad'e approximations of descriptor systems.