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IRKA is a Riemannian Gradient Descent Method
Petar Mlinarić, Christopher A. Beattie, Zlatko Drmač, Serkan Gugercin
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The iterative rational Krylov algorithm (IRKA) is a commonly used fixed-point iteration developed to minimize the ℋ₂ 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.
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