On tractability of weighted integration over bounded and unbounded regions in ℝs

Mathematics of Computation

Volumn 73, Issue 248, 2004, Pages 1885-1901

  Hickernell, Fred J ^a   Sloan, Ian H ^b   Wasilkowski, Grzegorz W ^c  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

^c UNIVERSITY OF KENTUCKY   (United States)

Author keywords

Discrepancy; quasi Monte Carlo methods; Tractability; Weighted integration

Indexed keywords

EID: 4444247206     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-04-01624-2     Document Type: Article

References (15)

1. M. Drmota and R. F. Tichy, Sequences, Discrepancies and Applications, Lecture Notes in Math. 1651, Springer, Berlin, 1997. MR 98j:11057
2. S. Heinrich, E. Novak, G. W. Wasilkowski, and H. Woźniakowski, The inverse of the star-discrepancy depends linearly on the dimension, Acta Arithmetica XCVI.3, pp. 279-302, 2001. MR 2002b:11103
3. F. H. Hickernell, A generalized discrepancy and quadrature error bound, Math. Comp. 67, pp. 299-322, 1998. MR 98c:65032
4. F. H. Hickernell, I. H. Sloan, and G. W. Wasilkowski, On tractability of integration for certain Banach spaces of functions, Monte Carlo and Quasi-Monte Carlo 2003 (H. Niederreiter, ed.), Springer 2003 (to appear).
5. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. MR 93h:65008
6. E. Novak, Deterministic and Stochastic Error Bounds in Numerical Analysis, Lecture Notes in Mathematics 1349, Springer, 1988. MR 90a:65004
7. E. Novak and H. Woźniakowski, Intractability results for integration and discrepancy, J. Complexity 17, pp. 388-441, 2001. MR 2002f:65204
8. S. H. Paskov, New methodologies for valuing derivatives, Mathematics of Derivative Securities (S. Pliska, M. Dempster eds.), pp. 545-582, Cambridge University Press, 1997.
9. S. H. Paskov and J. F. Traub, Faster valuation of financial securities, J. Portfolio Management 22, pp. 113-120, 1995.
10. D. Pollard, Convergence of Stochastic Processes, 1984, Springer Verlag. MR 86i:60074
11. I. H. Sloan, QMC integration - beating intractability by weighting the coordinate directions, Monte Carlo and Quasi-Monte Carlo Methods 2000 (K.-T. Fang, F. J. Hickernell, H. Niederreiter, eds.), pp. 103-123, Springer 2002.
12. I. H. Sloan and H. Woźniakowski, When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?, J. Complexity 14, pp. 1-33 (1998). MR 99d:65384
13. J. F. Traub and A. G. Werschulz, Complexity and Information, Cambridge University Press, 1998. MR 2000m:65170
14. J. F. Traub, G. W. Wasilkowski, and H. Woźniakowski, Information-Base Complexity, Academic Press, New York, 1988. MR 90f:68085
15. S. K. Zaremba, Some applications of multivariate integration by parts, Ann. Pol. Math. 21, pp. 95-96, 1968. MR 38:4034