IRKA Is a Riemannian Gradient Descent Method

• 成果类型: Article
• 署名作者: Mlinaric, Petar; Beattie, Christopher A.; Drmac, Zlatko; Gugercin, Serkan
• 署名单位: Virginia Polytechnic Institute & State University; University of Zagreb; Virginia Polytechnic Institute & State University; Virginia Polytechnic Institute & State University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3489416
• 发表日期: 2025
• 页码: 2979-2991
• 关键词: Read only memory; MANIFOLDS; interpolation; vectors; Eigenvalues and eigenfunctions; Stability criteria; Optimization methods; Numerical stability; Iterative algorithms; indexes; computational methods; Linear systems; optimization; reduced order modeling

摘要

The iterative rational Krylov algorithm (IRKA) is a commonly used fixed point iteration developed to minimize the H-2 model order reduction error. In this work, the 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 the IRKA and this extension on a few examples demonstrate significant benefits.