Optimal discrepancy rate of point sets in Besov spaces with negative smoothness
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Publication:1722531
DOI10.1007/978-3-319-91436-7_20zbMATH Open1448.46030arXiv1701.01970OpenAlexW2572767042MaRDI QIDQ1722531
Publication date: 18 February 2019
Abstract: We consider the local discrepancy of a symmetrized version of Hammersley type point sets in the unit square. As a measure for the irregularity of distribution we study the norm of the local discrepancy in Besov spaces with dominating mixed smoothness. It is known that for Hammersley type points this norm has the best possible rate provided that the smoothness parameter of the Besov space is nonnegative. While these point sets fail to achieve the same for negative smoothness, we will prove in this note that the symmetrized versions overcome this defect. We conclude with some consequences on discrepancy in further function spaces with dominating mixed smoothness and on numerical integration based on quasi-Monte Carlo rules.
Full work available at URL: https://arxiv.org/abs/1701.01970
Monte Carlo methods (65C05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Irregularities of distribution, discrepancy (11K38)
Related Items (1)
Discrepancy of generalized Hammersley type point sets in Besov spaces of dominating mixed smoothness
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