Convergence of the Iterative Rational Krylov Algorithm

Garret Flagg; Christopher Beattie; Serkan Gugercin

doi:10.1016/j.sysconle.2012.03.005

paper

Convergence of the Iterative Rational Krylov Algorithm

arXiv:1107.5363 · doi:10.1016/j.sysconle.2012.03.005

Abstract

The Iterative Rational Krylov Algorithm (IRKA) of [8] is an interpolatory model reduction approach to the optimal $H_{2}$ approximation problem. Even though the method has been illustrated to show rapid convergence in various examples, a proof of convergence has not been provided yet. In this note, we show that in the case of state-space symmetric systems, IRKA is a locally convergent fixed point iteration to a local minimum of the underlying $H_{2}$ approximation problem.