QMC Working Group X: Simpson Plays Billiards?

Group Leaders:
Dirk Nuyens (KU Leuven – Belgium)

Description:
Lattice rules are normally applied in the context of integrating periodic functions. There are however several results known in which lattice rules can be used in the context of non-periodic function spaces. We are interested in obtaining higher-order convergence for such non-periodic function spaces.

As a first wild idea, inspired by an interpretation of tent-transormed lattice rules as trapezoidal rules over a billiard ball trajectory, we might look at a fractal-transform which generates a Simpson’s rule. We are then interested in deriving worst-case error bounds which show higher-order convergence.

News and Updates: Coming soon…

SAMSI Directorate Liaison: Ilse Ipsen

Questions: email qmc@samsi.info

Program on Quasi-Monte Carlo and High-Dimensional Sampling Methods for Applied Mathematics (QMC)