Quadrature Error Bounds with Applications to Lattice Rules

Authors:
Fred J. Hickernell
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
1996

Citing 0
Cited 6

The mean square discrepancy of randomized nets

ACM Transactions on Modeling and Computer Simulation (TOMACS)
Quasi-Monte Carlo via linear shift-register sequences

Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future - Volume 1
On the root mean square weighted L2 discrepancy of scrambled nets

Journal of Complexity
Complexity and effective dimension of discrete Lévy areas

Journal of Complexity
Existence and construction of shifted lattice rules with an arbitrary number of points and bounded weighted star discrepancy for general decreasing weights

Journal of Complexity
Better estimation of small sobol' sensitivity indices

ACM Transactions on Modeling and Computer Simulation (TOMACS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

Reproducing kernel Hilbert spaces are used to derive error bounds and worst-case integrands for a large family of quadrature rules. In the case of lattice rules applied to periodic integrands these error bounds resemble those previously derived in the literature. However, the theory developed here does not require periodicity and is not restricted to lattice rules. An analysis of variance (ANOVA) decomposition is employed in defining the inner product. It is shown that imbedded rules are superior when integrating functions with large high-order ANOVA effects. Due to a printer's error, sections of this paper had to be reprinted. Those sections are available online.