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arXiv · 2311.02031

IRKA is a Riemannian Gradient Descent Method

Petar Mlinarić·Christopher A. Beattie·Zlatko Drmač·Serkan Gugercin
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Abstract

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.

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BibTeXRIS

Petar Mlinarić, Christopher A. Beattie, Zlatko Drmač, Serkan Gugercin. 2023-11-03. IRKA is a Riemannian Gradient Descent Method. https://arxiv.org/abs/2311.02031

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