Lattice Rules: How Well Do They Measure Up?

Fred J. Hickernell

Research output: Chapter in book/report/conference proceedingChapterpeer-review


A simple, but often effective, way to approximate an integral over the s-dimensional unit cube is to take the average of the integrand over some set P of N points. Monte Carlo methods choose P randomly and typically obtain an error of 0(N-1/2). Quasi-Monte Carlo methods attempt to decrease the error by choosing P in a deterministic (or quasi-random) way so that the points are more uniformly spread over the integration domain.
Original languageEnglish
Title of host publicationRandom and Quasi-Random Point Sets
EditorsPeter Hellekalek, Gerhard Larcher
Place of PublicationNew York
Number of pages58
ISBN (Electronic)9781461217022
ISBN (Print)9780387985541
Publication statusPublished - 9 Oct 1998
Externally publishedYes

Publication series

NameLecture Notes in Statistics
ISSN (Print)0930-0325
ISSN (Electronic)2197-7186

User-Defined Keywords

  • Quadrature Rule
  • Reproduce Kernel Hilbert Space
  • Star Discrepancy
  • Quadrature Error
  • Bernoulli Polynomial


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