High-Order QMC-PG Discretization of countably-parametric, nonlinear operator equations

Abstract: 

We survey recent results on high order QMC integration rules for direct and inverse problems of countably-parametric operator equations  with smooth parametric dependence.

We discuss aspects on their implementation and present first results on their computational performance, indicating in particular convergence rates 
independent of the dimension up to order four are feasible.

Joint work with Dick, Kuo, LeGia (UNSW), Nuyens (Leuven), Sloan (UNSW) and R. Gantner (ETH).