# Rational Krylov algorithms for eigenvalue computation and model reduction

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## 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.

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## References

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© Springer-Verlag Berlin Heidelberg 1998