Convergence of the Iterative Rational Krylov Algorithm

The iterative rational Krylov algorithm (IRKA) of Gugercin et al. (2008) [8] is an interpolatory model reduction approach to the optimal H2H2 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 H2H2 approximation problem.