Adaptive Tangential Interpolation in Rational Krylov Subspaces for MIMO Dynamical Systems

TLDR: An effective way to treat multiple inputs by dynamically choosing the next direction vectors to expand the space is presented and is competitive with respect to state-of-the-art methods both in terms of CPU time and memory requirements.

Abstract: Model reduction approaches have been shown to be powerful techniques in the numerical simulation of very large dynamical systems. The presence of multiple inputs and outputs (MIMO systems) makes the reduction process even more challenging. We consider projection-based approaches where the reduction of complexity is achieved by direct projection of the problem onto a rational Krylov subspace of significantly smaller dimension. We present an effective way to treat multiple inputs by dynamically choosing the next direction vectors to expand the space. We apply the new strategy to the approximation of the transfer matrix function and to the solution of the Lyapunov matrix equation. Numerical results confirm that the new approach is competitive with respect to state-of-the-art methods both in terms of CPU time and memory requirements.