UTA Department of Mathematics

Applied Mathematics Seminar

Date/Time/Room: Friday (2/10/2006) at 1:00pm in 304 Pickard Hall

Speaker: Dr. Ren-Cang Li, Associate Professor
Department of Mathematics, University of Kentucky

"Structural Preserving Numerical Methods for Model Reduction And Eigenvalue Problems"

Abstract: A general framework for structural preserving numerical methods for model reduction by Krylov subspace projections is developed. The goal is to preserve any substructures of importance in the matrices $L, G, C, B$ that define the model prescribed by transfer function $H(s)=L^*(G+s C)^{-1} B$. The framework also works for eigenvalue problems as model reduction and eigenvalue computation are deeply related. As an application, quadratic transfer functions targeted by Su and Craig (J. Guidance, Control, and Dynamics, 14 (1991), pp. 260--267.) is revisited, which leads to an improved algorithm than Su's and Craig's original one in terms of achieving the same approximation accuracy with smaller reduced systems. New Gram-Schmidt type orthogonalization process and new Arnoldi type process that only orthogonalize the prescribed portion of all basis vectors as opposing to whole vectors by existing counterparts are also developed. These new processes are designed as one way to numerically realize the idea in the general framework.