Abstract
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.
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- 1.
See also isp.m in the associated source code archive.
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Acknowledgements
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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Himpe, C., Ohlberger, M. (2017). Cross-Gramian-Based Model Reduction: A Comparison. In: Benner, P., Ohlberger, M., Patera, A., Rozza, G., Urban, K. (eds) Model Reduction of Parametrized Systems. MS&A, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-58786-8_17
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DOI: https://doi.org/10.1007/978-3-319-58786-8_17
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