Dirk Nuyens (KU Leuven – Belgium)
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.
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