Discrepancy-based error estimates for Quasi-Monte Carlo. II: Results in one dimension

Abstract

The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets with a discrepancy that is low with respect to the expected value for truly random point sets, are generally thought to be desirable. A low value of the discrepancy implies a negative correlation between the points, which may be usefully employed to improve the error estimate of a numerical integral based on the point set. We apply the formalism developed in a previous publication to compute this correlation for one-dimensional point sets, using a few different definitions of discrepancy.

10 pages, 3 Encapsulated Postscript figures, uses a4.sty,psfrag.sty+epsf.sty(coming with psfrag.sty)

References in corpus (1)

• Discrepancy-based error estimates for Quasi-Monte Carlo. I: General formalism

Cited by in corpus (5)

• Discrepancy-based error estimates for Quasi-Monte Carlo. III: Error distributions and central limits
• Error in Monte Carlo, quasi-error in Quasi-Monte Carlo
• Gaussian limits for discrepancies. I: Asymptotic results
• Quantum field theory for discrepancies
• Quantum field theory for discrepancies II: 1/N corrections using fermions