Friedrich Pillichshammer: Multivariante integration in weighted Hilbert spaces based on Walsh functions

This is a joint work with Josef Dick.

We present recent results on the quasi-Monte Carlo rules using digital nets for numerical integration. More detailed we introduce a weighted reproducing kernel Hilbert space which is based on Walsh functions and study the worst-case error for integration in this space, especially with regard to digital $ (t,m,s)$-nets. It is found that there exists a digital net, which achieves a strong tractability worst-case error bound under certain condition on the weights. Such a net can be constructed by a component-by-component algorithm.

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