  The iterative rational Krylov algorithm (IRKA) is a commonly used fixed-point
iteration developed to minimize the $\mathcal{H}_2$ model order reduction
error. In this work, IRKA is recast as a Riemannian gradient descent method
with a fixed step size over the manifold of rational functions having fixed
degree. This interpretation motivates the development of a Riemannian gradient
descent method utilizing as a natural extension variable step size and line
search. Comparisons made between IRKA and this extension on a few examples
demonstrate significant benefits.
