A structure preserving Krylov subspace method for Large Scale Differential Riccati Equations (Antti Koskela - KTH)
30.05.2017 14:15 – 15:15
We propose a Krylov subspace approximation method for the symmetric differential Riccati equation X' = AX + XA^T + Q + XSX, X(0)=X_0. The method is based on projecting the large scale equation onto a Krylov subspace spanned by the matrix A and the low rank factors of X_0 and Q.
We prove that the method is structure preserving in a sense that it preserves two important properties of the exact flow, namely the positivity of the exact flow, and also the monotonicity under certain conditions.
We also provide theoretical a priori error analysis of the method which shows a superlinear convergence. This behaviour is illustrated in the numerical experiments.
Moreover, we carry out a derivation of an efficient a posteriori error estimate as well as discuss the global error arising from multiple time stepping and from the cut of the rank of the numerical solution.
Lieu
Room 624, Séminaire d'analyse numérique
Organisé par
Section de mathématiquesIntervenant-e-s
Antti Koskela , KTHentrée libre