Adaptive rational interpolation: Restarting methods for a modified rational Arnoldi algorithm

An algorithm which belongs to the class of Krylov projection methods for model reduction of linear systems is the rational Arnoldi algorithm. The resulting reduced models approximate the dynamics of the full order system at different interpolation points and a careful selection of the interpolation points can result in good approximations. However, the order of the reduced system can be relatively high while the error of approximation remains unsatisfactory. In this paper we develope numerically efficient restart schemes which improve further the approximation without increasing the order of the approximation.