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An improved numerical method for balanced truncation for symmetric second-order systems

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  • Peter Benner
  • Patrick Kürschner
  • Jens Saak

Abstract

We consider balanced truncation model order reduction for symmetric second-order systems. The occurring large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank alternating directions implicit (ADI) type method. Stopping criteria for this iteration are investigated, and a new result concerning the Lyapunov residual within the low-rank ADI method is established. We also propose a goal-oriented stopping criterion which tries to incorporate the balanced truncation approach already during the ADI iteration. The model reduction approach using the ADI method with different stopping criteria is evaluated on several test systems.

Suggested Citation

  • Peter Benner & Patrick Kürschner & Jens Saak, 2013. "An improved numerical method for balanced truncation for symmetric second-order systems," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 19(6), pages 593-615, December.
    • Handle: RePEc:taf:nmcmxx:v:19:y:2013:i:6:p:593-615
    DOI: 10.1080/13873954.2013.794363
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    Cited by:

    1. N. Lang & J. Saak & T. Stykel, 2016. "Balanced truncation model reduction for linear time-varying systems," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 22(4), pages 267-281, July.

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