• Publications
  • Influence
A generalized discrepancy and quadrature error bound
TLDR
An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. Expand
  • 600
  • 62
  • PDF
Lattice rules: how well do they measure up? in random and quasi-random point sets
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 PExpand
  • 259
  • 25
Randomized Halton sequences
The Halton sequence is a well-known multi-dimensional low-discrepancy sequence. In this paper, we propose a new method for randomizing the Halton sequence. This randomization makes use of theExpand
  • 162
  • 11
The existence of good extensible rank-1 lattices
TLDR
We show that there exist generating vectors, h, for extensible rank-1 lattices such that for n = b, b2, ... points and dimensions s = 1, 2, ... the figures of merit Rα, Pα and discrepancy are all small. Expand
  • 77
  • 9
  • PDF
Control variates for quasi-Monte Carlo
Quasi-Monte Carlo (QMC) methods have begun to displace ordinary Monte Carlo (MC) methods in many practical problems. It is natural and obvious to combine QMC methods with traditional varianceExpand
  • 71
  • 9
  • PDF
Algorithm 823: Implementing scrambled digital sequences
TLDR
Random scrambling of deterministic (t, m, s)-nets and digital sequences eliminates their inherent bias while retaining their low-discrepancy properties. Expand
  • 110
  • 8
  • PDF
Uniform designs limit aliasing
When fitting a linear regression model to data, aliasing can adversely affect the estimates of the model coefficients and the decision of whether or not a term is significant. Optimal experimentalExpand
  • 103
  • 8
  • PDF
Integration and approximation in arbitrary dimensions
TLDR
We prove that integration is tractable for some weighted Korobov and Sobolev spaces as well as for the Hilbert space whose reproducing kernel corresponds to the covariance function of the isotropic Wiener measure. Expand
  • 115
  • 7
The mean square discrepancy of randomized nets
TLDR
In this article a formula for the mean square <italic>L</italic><supscrpt>2</sups crpt>-discrepancy of (<italic>(t, m, s) nets is derived. Expand
  • 66
  • 7
Time-dependent critical layers in shear flows on the beta-plane
The problem of a finite-amplitude free disturbance of an inviscid shear flow on the beta-plane is studied. Perturbation theory and matched asymptotics are used to derive an evolution equation for theExpand
  • 75
  • 7