Open problems for tractability of multivariate integration

Journal of Complexity

Volumn 19, Issue 3, 2003, Pages 434-444

  Woźniakowski, Henryk ^a,b  

^a Department of Earth and Environmental Sciences   (United States)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038730526     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0885-064X(03)00016-5     Document Type: Article

References (19)

1. N.S. Bakhvalov, On approximate computation of integrals, Vestnik MGU, Ser. Math. Mech. Astron. Phys. Chem. 4 (1959) 3-18 (in Russian).
2. S. Heinrich, Some open problems concerning the star-discrepancy (contribution to the open problem session, this issue).
3. S. Heinrich, E. Novak, G.W. Wasilkowski, H. Woźniakowski, The inverse of the star-discrepancy depends linearly on the dimension, Acta Arith. 96 (3) (2001) 279- 302.
4. F.J. Hickernell, H. Woźniakowski, Integration and approximation in arbitrary dimensions, Adv. Comput. Math. 12 (2000) 25-58.
5. F.Y. Kuo, Component-by-component constructions that achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces, J. Complexity, to appear.
6. F.Y. Kuo, Constructive approaches to quasi-Monte Carlo methods for multiple integration, Ph.D. Thesis, The University of Waikato, New Zealand, 2002.
7. F.Y. Kuo, S. Joe, Component-by-component construction of good lattice rules with a composite number of points, J. Complexity, to appear.
8. E. Novak, Deterministic and Stochastic Error Bounds in Numerical Analysis, in: Lecture Notes in Mathematics, Vol. 1349, Springer, Berlin, 1988.
9. E. Novak, Is there a curse of dimension for integration?, in: C.-H. Lai, P.E. Bjørstad, M. Cross, O.B. Widlund (Eds.), Eleventh International Conference on Domain Decomposition Methods, Domain Decomposition Press, Bergen, Norway, 1999, pp. 89-96.
10. E. Novak, H. Woźniakowski, When are integration and discrepancy tractable?, in: R.A. DeVore, A. Iserles, E. Süli (Eds.), Foundation of Computational Mathematics, Oxford, 1999, Cambridge University Press, Cambridge, 2001, pp. 211-266.
11. E. Novak, H. Woźniakowski, Intractability results for integration and discrepancy, J. Complexity 17 (2001) 388-441.
12. I.H. Sloan, F.Y. Kuo, S. Joe, On the step-by-step construction of quasi-Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces, Math. Comp., to appear.
13. I.H. Sloan, H. Woźniakowski, When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?, J. Complexity 14 (1998) 1-33.
14. I. H. Sloan, H. Woźniakowski, Tractability of multivariate integration for weighted Korobov classes, J. Complexity 17 (2001) 697-721.
15. I.H. Sloan, H. Woźniakowski, When does Monte Carlo depend polynomially on the number of variables?, submitted for publication.
16. J.F. Traub, G.W. Wasilkowski, H. Woźniakowski, Information-Based Complexity, Academic Press, New York, 1988.
17. J.F. Traub, A.G. Werschulz, Complexity and Information, Cambridge University Press, Cambridge, 1998.
18. G.W. Wasilkowski, H. Woźniakowski, Weighted tensor product algorithms for linear multivariate problems, J. Complexity 15 (1999) 402-447.
19. H. Woźniakowski, Efficiency of quasi-Monte Carlo algorithms for high dimensional integrals, in: H. Niederreiter, J. Spanier (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 1998, Springer, Berlin, 1999, pp. 114-136.