BIT Numerical Mathematics

, Volume 46, Supplement 1, pp 99–111

Rational Krylov for eigenvalue computation and model order reduction


DOI: 10.1007/s10543-006-0085-9

Cite this article as:
Olsson, K. & Ruhe, A. Bit Numer Math (2006) 46(Suppl 1): 99. doi:10.1007/s10543-006-0085-9


A rational Krylov algorithm for eigenvalue computation and model order reduction is described. It is shown how to implement it as a modified shift-and-invert spectral transformation Arnoldi decomposition. It is shown how to do deflation, locking converged eigenvalues and purging irrelevant approximations. Computing reduced order models of linear dynamical systems by moment matching of the transfer function is considered.

Results are reported from one illustrative toy example and one practical example, a linear descriptor system from a computational fluid dynamics application.

Key words

eigenvalue computation moment matching  Krylov sequence stability  

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Vehicle IntegrationSaab Automobile ABTrollhättanSweden
  2. 2.KTH – Numerical Analysis and Computer ScienceStockholmSweden

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