IRKA is a Riemannian Gradient Descent Method

2023/11/03 by Petar Mlinarić, Christopher Beattie, Mlinarić, Petar +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Electrical engineering #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2311.02031

openalex publication_date 2023/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• A reduced-IRKA method for large-scale H₂-optimal model order reduction

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