Inexact Solves in Interpolatory Model Reduction

Dynamical systems are mathematical models characterized by a set of differential or differ-ence equations. Due to the increasing demand for more accuracy, the number of equations involved may reach the order of thousands and even millions. With so many equations, it of-ten becomes computationally cumbersome to work with these large-scale dynamical systems. Model reduction aims to replace the original system with a reduced system of significantly smaller dimension which will still describe the important dynamics of the large-scale model. Interpolation is one method used to obtain the reduced order model. This requires that the reduced order model interpolates the full order model at selected interpolation points. Reduced order models are obtained through the Krylov reduction process, which involves solving a sequence of linear systems. The Iterative Rational Krylov Algorithm (IRKA) it-erates this Krylov reduction process to obtain an optimal H2 reduced model. Especially in the large-scale setting, these linear systems often require employing inexact solves. The aim of this thesis is to investigate the impact of inexact solves on interpolatory model reduction. We considered preconditioning the linear systems, varying the stopping tolerances, employin