Abstract
Rational Krylov is an extension of the Lanczos or Arnoldi eigenvalue algorithm where several shifts (matrix factorizations) are performed in one run. A variant has been developed, where these factorizations are performed in parallel.
It is shown how Rational Krylov can be used to find a reduced order model of a large linear dynamical system. In Electrical Engineering, it is important that the reduced model is accurate over a wide range of frequencies, and then Rational Krylov with several shifts comes to advantage.
Results for numerical examples coming from Electrical Engineering applications are demonstrated.
Partial support given by TFR, the Swedish Research Council for Engineering Sciences, Dnr 222, 96-555, and from the Royal Society of Arts and Sciences in Göteborg.
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Ruhe, A., Skoogh, D. (1998). Rational Krylov algorithms for eigenvalue computation and model reduction. In: Kågström, B., Dongarra, J., Elmroth, E., Waśniewski, J. (eds) Applied Parallel Computing Large Scale Scientific and Industrial Problems. PARA 1998. Lecture Notes in Computer Science, vol 1541. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095373
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DOI: https://doi.org/10.1007/BFb0095373
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