  Interpolation-based methods are well-established and effective approaches for
the efficient generation of accurate reduced-order surrogate models. Common
challenges for such methods are the automatic selection of good or even optimal
interpolation points and the appropriate size of the reduced-order model. An
approach that addresses the first problem for linear, unstructured systems is
the Iterative Rational Krylov Algorithm (IRKA), which computes optimal
interpolation points through iterative updates by solving linear eigenvalue
problems. However, in the case of preserving internal system structures,
optimal interpolation points are unknown, and heuristics based on nonlinear
eigenvalue problems result in numbers of potential interpolation points that
typically exceed the reasonable size of reduced-order systems. In our work, we
propose a projection-based iterative interpolation method inspired by IRKA for
generally structured systems to adaptively compute near-optimal interpolation
points as well as an appropriate size for the reduced-order system.
Additionally, the iterative updates of the interpolation points can be chosen
such that the reduced-order model provides an accurate approximation in
specified frequency ranges of interest. For such applications, our new approach
outperforms the established methods in terms of accuracy and computational
effort. We show this in numerical examples with different structures.
