Stable reduced-order models of generalized dynamical systems using coordinate-transformed Arnoldi algorithms

Model order reduction based on Krylov subspace iterative methods has recently emerged as a major tool for compressing the number of states in linear models used for simulating very large physical systems (VLSI circuits, electromagnetic interactions). There are currently two main methods for accomplishing such a compression: one is based on the nonsymmetric look-ahead Lanczos algorithm that gives a numerically stable procedure for finding Pade approximations, while the other is based on a less well characterized Arnoldi algorithm. In this paper, we show that for certain classes of generalized state-space systems, the reduced-order models produced by a coordinate-transformed Arnoldi algorithm inherit the stability of the original system. Complete Proofs of our results will be given in the final paper.