Abstract
We analyze a family of Runge-Kutta-based quadrature algorithms for the approximation of the Gramians of linear time-invariant dynamical systems. The approximated Gramians are used to obtain an approximate balancing transformation similar to the approach used in balanced POD. It is shown that hereby rational interpolation is performed, as the approximants span certain Krylov subspaces. The expansion points are mainly determined by the time step sizes and the eigenvalues of the matrices given by the Butcher tableaus.
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Bertram, C., Faßbender, H. (2021). A Link Between Gramian-Based Model Order Reduction and Moment Matching. In: Benner, P., Breiten, T., Faßbender, H., Hinze, M., Stykel, T., Zimmermann, R. (eds) Model Reduction of Complex Dynamical Systems. International Series of Numerical Mathematics, vol 171. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-72983-7_6
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