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QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. (English) Zbl 1186.65005
The aim of the paper is to show how some results of the second author can be achieved in a reproducing kernel Hilbert space setting. In particular, the authors consider numerical integration in a weighted Sobolev spaces and prove results about the worst-case error. Also they provide exact formulae and bounds for the integration errors, and present some numerical results for the test problems.

65C05 Monte Carlo methods
11K38 Irregularities of distribution, discrepancy
11K45 Pseudo-random numbers; Monte Carlo methods
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
65D32 Numerical quadrature and cubature formulas
Full Text: DOI
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