@Article{IJNAM-10-972,
author = {Y. Xu and T. Zeng},
title = {Fast Optimal $\mathcal{H}_2$ Model Reduction Algorithms Based on Grassmann Manifold Optimization},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {4},
pages = {972--991},
abstract = {<p style="text-align: justify;">The optimal $\mathcal{H}_2$ model reduction is an important tool in studying dynamical systems of a large order and their numerical simulation. We formulate the reduction problem as a minimization 
problem over the Grassmann manifold. This allows us to develop a fast gradient flow
algorithm suitable for large-scale optimal $\mathcal{H}_2$ model reduction problems. The proposed algorithm
converges globally and the resulting reduced system preserves stability of the original system.
Furthermore, based on the fast gradient flow algorithm, we propose a sequentially quadratic approximation 
algorithm which converges faster and guarantees the global convergence. Numerical
examples are presented to demonstrate the approximation accuracy and the computational efficiency 
of the proposed algorithms.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/606.html}
}