Discrepancy of generalized Hammersley type point sets in Besov spaces of dominating mixed smoothness
Numerical Analysis
2014-02-19 v4
Abstract
The symmetrized Hammersley point set is known to achieve the best possible rate for the -norm of the discrepancy function. Also lower bounds for the norm in Besov spaces of dominating mixed smoothness are known. In this paper a large class of point sets which are generalizations of the Hammersley type point sets are proved to asymptotically achieve the known lower bound of the Besov norm. The proof uses a -adic generalization of the Haar system. This result can be regarded as a preparation for the proof in arbitrary dimension.
Keywords
Cite
@article{arxiv.1109.4548,
title = {Discrepancy of generalized Hammersley type point sets in Besov spaces of dominating mixed smoothness},
author = {Lev Markhasin},
journal= {arXiv preprint arXiv:1109.4548},
year = {2014}
}