OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

"Model reduction by rational interpolation & low rank approximate solutions to large-scale Sylvester equations"
Michalis Frangos (Imperial College, London)

Abstract:
Krylov subspace projection methods are increasingly used for model reduction of large-scale linear systems. This presentation talks about the derivation of a set of simple equations for the rational Arnoldi algorithm, an algorithm which belongs to the class of Krylov subspace methods. This set of equations is proven to be useful for adaptive rational interpolation, error analysis and it allows the parameterization of the reduced order system in terms of a free parameter. In this presentation we suggest some choices of the free parameter to enhance the properties of the reduced order system and we suggest the use of the rational Krylov subspace techniques for the solution to large-scale Sylvester equations.