Monday, May 5th 2008, 13:00-14:00 PM in Celestijnenlaan 200A room 00.147, 3001 Leuven-Heverlee
GMRES for oscillatory differential equations
By Sheehan Olver (Univ. Oxford)
We consider using the generalized minimum residual method (GMRES) for computing oscillatory ordinary differential equations. This method minimizes the residual of the Krylov subspace associated with the differential formulation of the equation. It turns out that this mmethod actually improves as the oscillations increase, at the same asymptotic order as the number of iterations used. Standard Krylov subspace theory doesn't apply, since differential operators are unbounded. Thus we must also prove convergence of this approximation. This follows from a new theorem which proves conditions in which a function can be approximated pointwise by its own derivatives.
About the speaker:
Sheehan Olver recently completed his PhD on oscillatory integrals at the University of Cambridge (pending Stefan's decision as a member of the jury). He is currently a Junior Research Fellow of St.John's College and active as a postdoc in the group of Nick Trefethen at the Computing Laboratory in Oxford.