@Article{IJNAM-10-972, author = {}, 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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/606.html} }