F. J. Hickernell

Publications
Influence

A generalized discrepancy and quadrature error bound

F. J. Hickernell
Computer Science, Mathematics
Math. Comput.
1998

An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. Expand

Lattice rules: how well do they measure up? in random and quasi-random point sets

F. J. Hickernell
Mathematics
1998

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… Expand

Randomized Halton sequences

X. Wang, F. J. Hickernell
Mathematics
1 October 2000

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 the… Expand

The existence of good extensible rank-1 lattices

F. J. Hickernell, H. Niederreiter
Computer Science, Mathematics
J. Complex.
1 June 2003

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

Control variates for quasi-Monte Carlo

F. J. Hickernell, C. Lemieux, A. Owen
Mathematics
1 February 2005

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 variance… Expand

Algorithm 823: Implementing scrambled digital sequences

H. Hong, F. J. Hickernell
Computer Science
TOMS
1 June 2003

Random scrambling of deterministic (t, m, s)-nets and digital sequences eliminates their inherent bias while retaining their low-discrepancy properties. Expand

Uniform designs limit aliasing

F. J. Hickernell, M. Liu
Mathematics
1 December 2002

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 experimental… Expand

Integration and approximation in arbitrary dimensions

F. J. Hickernell, H. Wozniakowski
Mathematics, Computer Science
Adv. Comput. Math.
2000

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

The mean square discrepancy of randomized nets

F. J. Hickernell
Mathematics, Computer Science
TOMC
1 October 1996

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

Time-dependent critical layers in shear flows on the beta-plane

F. J. Hickernell
Physics
1 May 1984

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 the… Expand

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