Optimal quadrature for Haar wavelet spaces

Authors:
Stefan Heinrich;Fred J. Hickernell;Rong-Xian Yue
Affiliations:
FB Informatik, Universität Kaiserslautern, PF 3049, D-67653 Kaiserslautern, Germany;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China;College of Mathematical Science, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, China
Venue:
Mathematics of Computation
Year:
2004

Citing 12
Cited 7

Random number generation and quasi-Monte Carlo methods

Random number generation and quasi-Monte Carlo methods
On the numerical integration of Walsh series by number-theoretic methods

Mathematics of Computation
On the numerical integration of high-dimensional Walsh-series by quasi-Monte Carlo methods

Mathematics and Computers in Simulation - Special issue: Numerical probabilities
The mean square discrepancy of randomized nets

ACM Transactions on Modeling and Computer Simulation (TOMACS)
Optimal Polynomials for (t,m,s)-Nets and Numerical Integration of Multivariate Walsh Series

SIAM Journal on Numerical Analysis
Monte Carlo Variance of Scrambled Net Quadrature

SIAM Journal on Numerical Analysis
Scrambling sobol' and niederreiter-xing points

Journal of Complexity
The asymptotic efficiency of randomized nets for quadrature

Mathematics of Computation
Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing: Proceedings of a Conference at the University of Nevada, Las Vegas, Nevada, USA, June 23-25, 1994

Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing: Proceedings of a Conference at the University of Nevada, Las Vegas, Nevada, USA, June 23-25, 1994
The Mean Square Discrepancy of Scrambled (t,s)-Sequences

SIAM Journal on Numerical Analysis
The discrepancy and gain coefficients of scrambled digital nets

Journal of Complexity
Quasi-Monte Carlo methods for the numerical integration of multivariate walsh series

Mathematical and Computer Modelling: An International Journal

Integration of Multivariate Haar Wavelet Series

WAA '01 Proceedings of the Second International Conference on Wavelet Analysis and Its Applications
My dream quadrature rule

Journal of Complexity
I-binomial scrambling of digital nets and sequences

Journal of Complexity
Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces

Journal of Complexity
Quasi-Monte Carlo methods in finance

WSC '04 Proceedings of the 36th conference on Winter simulation
Cubature formulas for function spaces with moderate smoothness

Journal of Complexity
Quasi-Monte Carlo Numerical Integration on $\mathbb{R}^s$: Digital Nets and Worst-Case Error

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

This article considers the error of the scrambled equidistribution quadrature rules in the worst-case, random-case, and average-case settings. The underlying space of integrands is a Hilbert space of multidimensional Haar wavelet series, Hwav. The asymptotic orders of the errors are derived for the case of the scrambled (λ, t, m, s)-nets and (t, s)-sequences. These rules are shown to have the best asymptotic convergence rates for any random quadrature rule for the space of integrands Hwav.