IRKA is a Riemannian Gradient Descent Method

Autor:	Mlinarić, Petar, Beattie, Christopher A., Drmač, Zlatko, Gugercin, Serkan
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis Electrical Engineering and Systems Science - Systems and Control Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.02031 Zobrazit plný text záznamu View this record from Arxiv