Reducing the construction cost of the component-by-component construction of good lattice rules

Mathematics of Computation

Volumn 73, Issue 248, 2004, Pages 1967-1988

  Dick, J ^a   Kuo, F Y ^a,b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF WAIKATO   (New Zealand)

Author keywords

Lattice rules; Numerical integration; Quasi Monte Carlo

Indexed keywords

EID: 3242686198     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-03-01610-7     Document Type: Article

References (14)

1. Aronszajn, N. (1950). Theory of reproducing kernels, Trans. Amer. Math. Soc., 68, 337-404. MR 14:479c
2. Dick, J. (2003). On the convergence rate of the component-by-component construction of good lattice rules, J. Complexity, submitted.
3. Hardy, G. H., Littlewood, J. E. and Pólya, G. (1934). Inequalities, Cambridge University Press, Cambridge.
4. Hickernell, F. J. and Hong, H. S. (2002). Quasi-Monte Carlo methods and their randomizations, Applied Probability (R. Chan, Y.-K. Kwok, D. Yao, and Q Zhang, eds.), AMS/IP Studies in Advanced Mathematics 26, American Mathematical Society, Providence, 59-77.
5. Hua, L. K. and Wang, Y. (1981). Applications of number theory to numerical analysis, Springer Verlag, Berlin; Science Press, Beijing. MR 83g: 10034
6. Korobov, N. M. (1960). Properties and calculation of optimal coefficients, Doklady Akademii Nauk SSSR, 132, 1009-10 (Russian). English transl.: Soviet Mathematics Doklady, 1, 696-700. MR 22:11517
7. Korobov, N. M. (1960). Properties and calculation of optimal coefficients, Doklady Akademii Nauk SSSR, 132, 1009-10 (Russian). English transl.: Soviet Mathematics Doklady, 1, 696-700. MR 22:11517
8. Kuo, F. Y. (2003). Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces, J. Complexity, 19, 301-320.
9. Kuo, F. Y. and Joe, S. (2002). Component-by-component construction of good lattice rules with a composite number of points, J. Complexity, 18, 943-976.
10. Sloan, I. H., Kuo, F. Y. and Joe, S. (2002). On the step-by-step construction of quasi-Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces, Math. Comp., 71, 1609-1640.
11. Sloan, I. H., Kuo, F. Y. and Joe, S. (2002). Constructing randomly shifted lattice rules in weighted Sobolev spaces, SIAM J. Numer. Anal., 40, 1650-1665.
12. Sloan, I. H., Retzsov, A. V. (2002). Component-by-component construction of good lattice points, Math. Comp., 71, 263-273. MR 2002h:65028
13. Sloan, I. H. and Woźniakowski, H. (1998). When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?, J. Complexity, 14, 1-33. MR 99d:65384
14. Sloan, I. H. and Woźniakowski, H. (2001). Tractability of multivariate integration for weighted Korobov classes, J. Complexity, 17, 697-721.