  The Iterative Rational Krylov Algorithm (IRKA) of [8] is an interpolatory
model reduction approach to the optimal $\mathcal{H}_2$ 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
$\mathcal{H}_2$ approximation problem.
