The existence of good extensible rank-1 lattices

Journal of Complexity

Volumn 19, Issue 3, 2003, Pages 286-300

  Hickernell, Fred J ^a   Niederreiter, Harald ^b  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Discrepancy; Extensible lattices; Figures of merit; Lattice rules; Quasi Monte Carlo integration

Indexed keywords

EID: 0037648331     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0885-064X(02)00026-2     Document Type: Article

References (14)

1. F.J. Hickernell, Lattice rules: how well do they measure up?, in: P. Hellekalek, G. Larcher (Eds.), Random and Quasi-Random Point Sets, Lecture Notes in Statistics, Vol. 138, Springer, New York, 1998, pp. 109-166.
2. F.J. Hickernell, H.S. Hong, Computing multivariate normal probabilities using rank-1 lattice sequences, in: G.H. Golub, S.H. Lui, F.T. Luk, R.J. Plemmons (Eds.), Proceedings of the Workshop on Scientific Computing (Hong Kong), Springer, Singapore, 1997, pp. 209-215.
3. F.J. Hickernell, H.S. Hong, P. L'Écuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2000) 1117-1138.
4. F.J. Hickernell, X. Wang, The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension, Math. Comput. 71 (2002) 1641-1661.
5. L.K. Hua, Y. Wang, Applications of Number Theory to Numerical Analysis, Springer, Science Press, Berlin, Beijing, 1981.
6. G. Larcher, A best lower bound for good lattice points, Monatsh. Math. 104 (1987) 45-51.
7. K. Mahler, Introduction to p-adic Numbers and their Functions, Cambridge Tracts in Mathematics, Vol. 64, Cambridge University Press, Cambridge, 1973.
8. H. Niederreiter, Existence of good lattice points in the sense of Hlawka, Monatsh. Math. 86 (1978) 203-219.
9. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 63, SIAM, Philadelphia, 1992.
10. H. Niederreiter, Improved error bounds for lattice rules, J. Complexity 9 (1993) 60-75.
11. I.F. Sharygin, A lower estimate for the error of quadrature formulas for certain classes of functions, Zh. Vychisl. Mat. i Mat. Fiz. 3 (1963) 370-376 (in Russian).
12. I.H. Sloan, S. Joe, Lattice Methods for Multiple Integration, Oxford University Press, Oxford, 1994.
13. I.H. Sloan, A.V. Reztsov, Component-by-component construction of good lattice rules, Math. Comput. 71 (2002) 263-273.
14. I.H. Sloan, H. Woźniakowski, Tractability of multivariate integration for weighted Korobov classes, J. Complexity 17 (2001) 697-721.