A New Analysis on PVL Model Reduction Using Solutions of Linear Systems by the Lanczos Method

It is theoretically well known that PVL model reduction is locally effective, but it may perform quite well globally in practice. This phenomenon is not well understood. In this paper, we give a solid theoretical analysis for the convergence of PVL model reduction. We transform it to the solution of parametrized linear systems by the nonsymmetric Lanczos method. We establish a result on its local effectiveness and shed lights on its possible global effectiveness. So our analysis gives more theoretical insights into the convergence or effectiveness of PVL model reduction.