Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Optimal quadrature for Haar wavelet spaces


Authors: Stefan Heinrich, Fred J. Hickernell and Rong-Xian Yue
Journal: Math. Comp. 73 (2004), 259-277
MSC (2000): Primary 65C05, 65D30
Published electronically: April 28, 2003
MathSciNet review: 2034121
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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, $\mathcal{H}_{\text{wav}}$. The asymptotic orders of the errors are derived for the case of the scrambled $(\lambda,t,m,s)$-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 $\mathcal{H}_{\text{wav}}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65C05, 65D30

Retrieve articles in all journals with MSC (2000): 65C05, 65D30


Additional Information

Stefan Heinrich
Affiliation: FB Informatik, Universität Kaiserslautern, PF 3049, D-67653 Kaiserslautern, Germany
Email: heinrich@informatik.uni-kl.de

Fred J. Hickernell
Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China
Email: fred@hkbu.edu.hk

Rong-Xian Yue
Affiliation: College of Mathematical Science, Shanghai Normal University, 100 Guilin Road, Shanghai 200234, China
Email: rxyue@online.sh.cn

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01531-X
PII: S 0025-5718(03)01531-X
Keywords: Quasi-Monte Carlo methods, Monte Carlo methods, high dimensional integration, lower bounds
Received by editor(s): July 9, 2001
Received by editor(s) in revised form: May 13, 2002
Published electronically: April 28, 2003
Additional Notes: This work was partially supported by a Hong Kong Research Grants Council grant HKBU/2030/99P, by Hong Kong Baptist University grant FRG/97-98/II-99, by Shanghai NSF Grant 00JC14057, and by Shanghai Higher Education STF grant 01D01-1.
Article copyright: © Copyright 2003 American Mathematical Society