Speaker
Description
The Loewner framework is one of the most successful data-driven model order reduction techniques.
Given $k$ right interpolation data and $h$ left interpolation data, the standard layout of this approach is composed of two stages.
First, the $kh\times kh$ Loewner matrix $\mathbb{L}$ and shifted Loewner matrix $\mathbb{L}_s$ are constructed. Then, an SVD of $\mathbb{L}_s-\gamma \mathbb{L}$, $\gamma\in\mathbb{C}$ belonging to one of the data sets, provides the projection matrices used to compute the sought reduced model.
These two steps become numerically challenging for large $k$ and $h$ in terms of both computational time and storage demand.
We show how the structure of $\mathbb{L}$ and $\mathbb{L}_s$ can be exploited to reduce the cost of performing $(\mathbb{L}_s-\gamma\mathbb{L})x$ while avoiding the explicit allocation of $\mathbb{L}$ and $\mathbb{L}_s$.
