Exact cubature for a class of functions of maximum effective dimension

被引：1
作者：
Tezuka, Shu
Papageorgiou, Anargyros
机构：
[1] Kyushu Univ, Fac Math, Higashi Ku, Fukuoka 8128581, Japan
[2] Columbia Univ, Dept Comp Sci, New York, NY 10027 USA
来源：
JOURNAL OF COMPLEXITY | 2006年 / 22卷 / 05期
关键词：
ANOVA; antisymmetric functions; effective dimension; high-dimensional integrals;
D O I：
10.1016/j.jco.2006.04.002
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We consider high-dimensional integration in a broad class of functions where all elements have maximum effective dimension. We show that there exists an exact cubature with only two points. Therefore, not only the convergence but also the worst case error of quasi-Monte Carlo need not depend on the effective dimension at all. (C) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：652 / 659
页数：8
相关论文
共 20 条
  • [1] Caflisch R. E., 1997, Journal of Computational Finance, V1, P27
  • [2] Liberating the weights
    Dick, J
    Sloan, IH
    Wang, XQ
    Wozniakowski, H
    [J]. JOURNAL OF COMPLEXITY, 2004, 20 (05) : 593 - 623
  • [3] Hellekalek P., 1998, Random and Quasi-Random Point Sets, P109, DOI [DOI 10.1007/978-1-4612-1702-2_3, 10.1007/978-1-4612-1702-2_3]
  • [4] Hickernell FJ, 2002, MATH COMPUT, V71, P1641, DOI 10.1090/S0025-5718-01-01377-1
  • [5] Kuo F, 2005, LIFTING CURSE DIMENS
  • [6] Monte Carlo variance of scrambled net quadrature
    Owen, AB
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (05) : 1884 - 1910
  • [7] Owen AB, 2003, STAT SINICA, V13, P1
  • [8] OWEN AB, 2002, NECESSITY LOW EFFECT
  • [9] Sufficient conditions for fast quasi-Monte Carlo convergence
    Papageorgiou, A
    [J]. JOURNAL OF COMPLEXITY, 2003, 19 (03) : 332 - 351
  • [10] PASKOV SH, 1997, MATH DERIVATIVE SECU, P545
12