Rational Krylov algorithms for eigenvalue computation and model reduction

  • Axel Ruhe
  • Daniel Skoogh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1541)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Axel Ruhe
    • 1
  • Daniel Skoogh
    • 1
  1. 1.Department of MathematicsChalmers Institute of Technology and the University of GöteborgGöteborgSweden

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