Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy

Stephen Joe ()
Additional contact information
Stephen Joe: University of Waikato, Department of Mathematics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 181-196 from Springer

Abstract: Summary The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrepancy. If the weights for the weighted star discrepancy are summable, then we show that for n prime there exist n-point rank-1 lattice rules whose weighted star discrepancy is O(n−1+δ) for any δ>0, where the implied constant depends on δ and the weights, but is independent of d and n. Further, we show that the generating vector z for such lattice rules may be obtained using a component-by-component construction. The results given here for the weighted star discrepancy are used to derive corresponding results for a weighted Lp discrepancy.

Keywords: Prime Number; Generate Vector; Reproduce Kernel Hilbert Space; Quadrature Point; Star Discrepancy (search for similar items in EconPapers)
Date: 2006
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_12

Ordering information: This item can be ordered from
http://www.springer.com/9783540311867

DOI: 10.1007/3-540-31186-6_12

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().