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 to the cross Gramian itself.
Cite
@article{arxiv.1606.03954,
title = {Cross-Gramian-Based Model Reduction: A Comparison},
author = {Christian Himpe and Mario Ohlberger},
journal= {arXiv preprint arXiv:1606.03954},
year = {2016}
}