Quadrature error bounds with applications to lattice rules

被引:39
作者
Hickernell, FJ
机构
[1] Department of Mathematics, Hong Kong Baptist University, Kowloon Tong
关键词
ANOVA decomposition; good lattice points; imbedded rules; multidimensional integration; Monte Carlo; number-theoretic; quasirandom; periodic functions; reproducing kernel Hilbert spaces;
D O I
10.1137/S0036142994261439
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:1995 / 2016
页数:22
相关论文
共 29 条
[11]  
Hlawka E., 1962, MONATSH MATH, V66, P140, DOI DOI 10.1007/BF01387711
[12]  
HUA LK, 1981, APPLICATIONS NUMBER
[13]   INTERMEDIATE RANK LATTICE RULES FOR MULTIDIMENSIONAL INTEGRATION [J].
JOE, S ;
DISNEY, SAR .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1993, 30 (02) :569-582
[14]   IMBEDDED LATTICE RULES FOR MULTIDIMENSIONAL INTEGRATION [J].
JOE, S ;
SLOAN, IH .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (04) :1119-1135
[15]  
JOE S., 1994, LATTICE METHODS MULT
[16]  
KOROBOV NM, 1959, DOKL AKAD NAUK SSSR+, V124, P1207
[17]   QUASI-RANDOM SEQUENCES AND THEIR DISCREPANCIES [J].
MOROKOFF, WJ ;
CAFLISCH, RE .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1994, 15 (06) :1251-1279
[18]   INTEGRATION OF NONPERIODIC FUNCTIONS OF 2 VARIABLES BY FIBONACCI LATTICE RULES [J].
NIEDERREITER, H ;
SLOAN, IH .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1994, 51 (01) :57-70
[19]  
NIEDERREITER H, 1990, MATH COMPUT, V54, P303, DOI 10.1090/S0025-5718-1990-0995212-4
[20]  
NIEDERREITER H, 1993, INT S NUM M, V112, P253