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Rational Krylov-subspace methods are a predestined candidate in the reduction of very-large-scale linear models due to their moderate computational cost and memory requirements. However, in order to achieve good approximation results, state-of-the-art Krylov algorithms like IRKA iteratively search for a set of locally H2-optimal reduction parameters. This search requires the repeated reduction of...
A method to preserve stability in parametric model order reduction by matrix interpolation for the whole parameter range is proposed for high-order linear time-invariant systems. In the first step, system matrices of the high-dimensional parameter-dependent system are computed for a discrete set of parameter vectors. The local high-order systems are reduced by a projection-based reduction method....
We present rigorous bounds on the ℌ2 and ℌ∞ norm of the error resulting from model order reduction of second order systems by KRYLOV subspace methods. To this end, we use a strictly dissipative state space realization of the model and perform a factorization of the error system. The derived error expressions are easy to compute and can therefore be applied to models of very high order, as is demonstrated...
New sufficient conditions for ℌ2 pseudo-optimality in Krylov-based model reduction of linear dynamical systems are presented. The conditions are easy to evaluate and permit first applications: a new algorithm to generate ℌ2 pseudo-optimal reduced models with respect to the projecting subspace and a procedure to generate superior local optima in iterative methods. Numerical examples illustrate the...
We present a new approach to the problem of finding suitable expansion points in Krylov subspace methods for the model reduction of LTI systems. Using a factorized formulation of the resulting error model, we can efficiently apply a greedy algorithm and perform multiple reduction steps instead of looking for all shifts at once. An expedient globally convergent optimization algorithm delivers locally...
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