Structure-aware Krylov approximations to generalized Cayley transforms

by Prof. Andreas Frommer (University of Wuppertal)

Friday 25 Oct 2024, 11:00 → 12:00 Europe/Rome

Aula Mancini (Scuola Normale Superiore)

Generalized Cayley transforms arise in implicit numerical integration schemes for ordinary differential equations and differential-algebraic equations. We consider Arnoldi-type methods to approximate the action of such a Cayley transform on a vector and investigate how energy conservation or dissipation can be enforced at the level of each Arnoldi iterate, not just at the level of the exact solution. We also investigate generalizations to higher order collocation methods.