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

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

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

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

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

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

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 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