Inexact Solves in Krylov-based Model Reduction

We investigate the use of inexact solves in a Krylov-based model reduction setting and present the resulting perturbation effects on the underlying model reduction problem. We show that for a good selection of interpolation points, Krylov-based model reduction is robust with respect to the perturbations due to inexact solves. On the other hand, when the interpolation points are poorly selected, these perturbations are magnified through the model reduction process. Finally, we incorporate inexact solves for the Krylov-based optimal H₂ approximation. The result is an effective optimal model reduction algorithm applicable in realistic large-scale settings