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— We introduce the random Weyl sampling. It is a sampling method that uses a sequence {x + na}^=Q on fc-dimensional torus T* = [0, l) where the pair of parameters (z, α) is considered to be random governed by the uniform measure on T*. It turns out that the random Weyl sampling has almost the same probabilistic error estimate for all square-integrable functions s the i.i.d.-sampling does. A remarkable point is that the random Weyl sampling requires much fewer pseudo-random numbers than the i.i.d.sampling does, and hence it is much less sensitive to their quality. We characterize the desirable pair (χ, α) for the purpose in terms of computational complexity.

Random Weyl sampling for robust numerical integration of complicated functions