The First VT Symposium on Reduced-Order Modeling and System Identification

1:30 Inexact Solves in Interpolatory Model Reduction, SERKAN GUGERCIN, CHRISTOPHER BEATTIE, AND SARAH WYATT (Department of Mathematics). We expand upon the work of Beattie and Gugercin, who examined the role of inexact solves in the interpolation-based model reduction setting. We show the effect of inexact solves in one-sided and two-sided interpolation-based reduction as well as for the optimal H2 approach. We consider preconditioning the linear systems, varying the stopping tolerances, employing GMRES and BiCG as the inexact solvers, and using different initial shift selections. We illustrate the importance of the Petrov-Galerkin framework in this setting and discuss the resulting backward error formulation from a systems theory perspective. Finally, we discuss our conclusions from several numerical simulations.