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We analyze a family of Runge-Kutta based quadrature algorithms for theapproximation of the gramians of linear time invariant dynamical systems. Theapproximated gramians are used to obtain an approximate balancingtransformation similar to the approach used in balanced POD. It is shown thathereby rational interpolation is performed, as the approximants span certainKrylov subspaces. The expansion points are mainly determined by the time stepsizes and the eigenvalues of the matrices given by the Butcher tableaus.

A link between gramian based model order reduction and moment matching