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We study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with general weights. These spaces are not necessarily tensor products of spaces of univariate functions. Sufficient conditions for tractability and strong tractability of multivariate integration in such weighted function spaces are found.(More)
This paper provides a novel approach to the construction of good lattice rules for the integration of Korobov classes of periodic functions over the unit s-dimensional cube. Theorems are proved which justify the construction of good lattice rules one component at a time – that is, the lattice rule for dimension s + 1 is obtained from the rule for dimension(More)
We define a Walsh space which contains all functions whose partial mixed derivatives up to order δ ≥ 1 exist and have finite variation. In particular, for a suitable choice of parameters, this implies that certain reproducing kernel Sobolev spaces are contained in these Walsh spaces. For this Walsh space we then show that quasi-Monte Carlo rules based on(More)
We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichsham-mer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special(More)
In this paper we give first explicit constructions of point sets in the s dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the worst-case error for numerically integrating high dimensional periodic functions. In the classical measure P α of the worst-case error introduced by Korobov in 1959 the(More)