Rational Krylov Methods for Optimal H2 Model Reduction

We develop and describe an iteratively corrected rational Krylov algorithm for the solution of the optimal H2 model reduction problem. The formulation is based on finding a reduced order model that satisfies interpolation based first-order necessary conditions for H2 optimality and results in a method that is numerically effective and suited for large-scale problems. We provide a new elementary proof of the interpolation based condition that clarifies the importance of the mirror images of the reduced system poles. We also show that the interpolation based condition is equivalent to two types of first-order necessary conditions associated with Lyapunov-based approaches for H2 optimality. Under some technical hypotheses, local convergence of the algorithm is guaranteed for sufficiently large model order with a linear rate that decreases exponentially with model order. We illustrate the performance of the method with a variety of numerical experiments and comparisons with existing methods.