The structure exploiting arnoldi algorithm for model order reduction of general higher-order linear dynamical systems

One possible model reduction technique for large-scale higher-order linear dynamical systems is to transform a given higher-order system into an equivalent first-order formulation. The desired reduced-order models are then constructed by employing Krylov subspace-based reduction methods to the resulting first-order system. Since the Krylov subspaces associated with these first-order systems can be viewed as multiple copies of the same underlying space, this technique can be improved. This research focuses on creating a Structure Exploiting Arnoldi (SEA) algorithm that generates an orthonormal basis for the aforementioned multiple-copied subspace. The SEA algorithm is a modification of the Arnoldi algorithm designed to perform updates using key properties of Krylov subspaces associated with general higher-order linear dynamical systems. Applications of this research include reduced-order modeling of both lth-order linear dynamical systems as well as systems of first-order integro-differential-algebraic equations.