A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets

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• 作者：Peter Kritzer ; Gerhard Larcher and Friedrich Pillichshammer
• 关键词：Discrepancy ; Hammersley net ; van der Corput sequence ; Distance to the nearest integer
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2007
• 出版时间：April, 2007
• 年：2007
• 卷：186
• 期：2
• 页码：229-250
• 全文大小：350 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1618-1891

文摘

We study the star discrepancy of Hammersley nets and van der Corput sequences which are important examples of low-dimensional quasi-Monte Carlo point sets. By a so-called digital shift, the quality of distribution of these point sets can be improved. In this paper, we advance and extend existing bounds on digitally shifted Hammersley and van der Corput point sets and establish criteria for the choice of digital shifts leading to optimal results. Our investigations are partly based on a close analysis of certain sums of distances to the nearest integer.