Gramian-based error bound in model reduction by Krylov subspace methods

• DOI: 10.3182/20110828-6-it-1002.02809
• Publication Date: 2011-08-28T20:55:44Z
• Authors: Thomas Wolf; Heiko Panzer; Boris Lohmann
• Keywords: 0101 mathematics; 01 natural sciences

Abstract In this paper, a factorization of the error system resulting from model order reduction by Krylov subspace methods is presented. It is shown that the first factor is a system equal to the original one except for the input vector, while the second factor is of reduced order. This enables a new analysis of the error system: Provided that the Observability Gramian of the original system has once been calculated, an H2 error bound can be computed with negligible numerical effort for any reduced model resulting from Krylov subspace methods. The new results can therefore be ideally applied to SVD-Krylov methods where the Gramian is available anyway. In addition, it is proven that the bound even matches the exact error value for H2 optimal reduced order models. A numerical example is used to demonstrate the potential of the new error bound.