Cross-Gramian-Based Model Reduction: A Comparison

  • Christian HimpeEmail author
  • Mario Ohlberger
Part of the MS&A book series (MS&A, volume 17)


As an alternative to the popular balanced truncation method, the cross Gramian matrix induces a class of balancing model reduction techniques. Besides the classical computation of the cross Gramian by a Sylvester matrix equation, an empirical cross Gramian can be computed based on simulated trajectories. This work assesses the cross Gramian and its empirical Gramian variant for state-space reduction on a procedural benchmark based on the cross Gramian itself.



This work was supported by the Deutsche Forschungsgemeinschaft: DFG EXC 1003 Cells in Motion - Cluster of Excellence, Münster, Germany and by the Center for Developing Mathematics in Interaction, DEMAIN, Münster, Germany.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany

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