Model-order reduction of large-scale kth-order linear dynamical systems via a kth-order Arnoldi method

In this paper, we first introduce a kth-order Krylov subspace 𝒢 n (A j ; u) based on a square matrix sequence {A j } and a vector u. Then we present a kth-order Arnoldi procedure for generating an orthonormal basis of 𝒢 n (A j ; u). By applying the projection technique, we derive a structure-preserving kth-order Arnoldi method for reduced-order modelling of the large-scale kth-order linear dynamical system. Applications to polynomial eigenvalue problems are also included. Numerical experiments report the effectiveness of this method.

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