Seminar Details
2026-02-03 (14:00) : IRKA Is a Riemannian Gradient Descent Method
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Petar Mlinarić (University of Zagreb)
Abstract :
Large-scale systems frequently arise in applications involving partial differential equations or network dynamics. Model order reduction seeks to replace a large-scale system with a reduced-order model, enabling faster simulations with minimal loss of accuracy. The Iterative Rational Krylov Algorithm (IRKA) is a well-known method for model order reduction of linear time-invariant systems, originally formulated as a fixed-point iteration. In this talk, we show that IRKA can be interpreted as a Riemannian gradient descent method with a fixed step size on the manifold of rational functions of fixed degree. This geometric perspective motivates the application of other Riemannian optimization techniques to the same problem. We illustrate the effectiveness of these approaches through numerical examples.