Intractability Results for Integration and Discrepancy

Journal of Complexity

Volumn 17, Issue 2, 2001, Pages 388-441

  Novak, Erich ^a   Wozniakowski H ^b  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035373628     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.2000.0577     Document Type: Article

References (27)

1. Aronszajn N. Theory of reproducing kernels. Trans. Amer. Math. Soc. 68:1950;337-404.
2. Bungartz H.-J., Griebel M. A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives. J. Complexity. 15:1999;167-199.
3. Drmota M., Tichy R. Sequences, Discrepancies, and Applications. Lecture Notes in Mathematics. 1651:1997;Springer-Verlag, Berlin.
4. p, 2≤p<∞ Dokl. Akad. Nauk SSSR. 252:1980;805-807.
5. Heinrich S., Novak E., Wasilkowski G. W., Woźniakowski H. The inverse of the star-discrepancy depends linearly on the dimension. Acta Arith. 96:2001;297-302.
6. Hickernell F. J. A generalized discrepancy and quadrature error bound. Math. Comp. 67:1998;299-322.
7. Hickernell F. J., Woźniakowski H. Integration and approximation in arbitrary dimension. Adv. Comput. Math. 12:2000;25-58.
8. Niederreiter H. Random Number Generation and Quasi-Monte Carlo Methods. 1992;SIAM, Philadelphia.
9. Novak E. Intractability results for positive quadrature formulas and extremal problems for trigonometric polynomials. J. Complexity. 15:1999;299-316.
10. Novak E. Is there a curse of dimension for integration? Lai C.-H., Bjørstad P. E., Cross M., Widlund O. B. Eleventh Int. Conf. on Domain Decomposition Methods. 1999;89-96.
11. Novak E., Sloan I. H., Woźniakowski H. Tractability of tensor product linear operators. J. Complexity. 13:1997;387-418.
12. Novak E., Woźniakowski H. When are integration and discrepancy tractable? Proc. of the FoCM conference. July 1999.
13. Roth K. F. On irregularities of distributions. Mathematika. 1:1954;73-79.
14. Roth K. F. On irregularities of distributions IV. Acta Arith. 37:1980;67-75.
15. Sloan I. H., Woźniakowski H. An intractability result for multiple integration. Math. Comp. 66:1997;1119-1124.
16. Sloan I. H., Woźniakowski H. When are quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complexity. 14:1998;1-33.
17. Tezuka S. Financial applications of Monte Carlo and quasi-Monte Carlo methods. Hellekalek P., Larcher G. Random and Quasi-Random Point Sets. Lecture Notes in Statistics. 138:1998;303-332 Springer, New York.
18. Thomas-Agnan C. Computing a family of reproducing kernels for statistical applications. Numerical Algorithms. 13:1996;21-32.
19. Traub J. F., Wasilkowski G. W., Woźniakowski H. Information-Based Complexity. 1988;Academic Press, San Diego.
20. Traub J. F., Werschulz A. G. Complexity and Information. 1998;Cambridge University Press, Cambridge.
21. Wahba G. Spline Models for Observational Data. SIAM-NSF Regional Conference Series in Appl. Math. 59:1990;SIAM, Philadelphia.
22. Wasilkowski G. W., Woźniakowski H. Explicit cost bounds of algorithms for multivariate tensor product problems. J. Complexity. 11:1995;1-56.
23. Wasilkowski G. W., Woźniakowski H. Weighted tensor-product algorithms for linear multivariate problems. J. Complexity. 15:1999;402-447.
24. Werschulz A. G. The complexity of the Poisson problem for spaces of bounded mixed derivatives. Renegar J., Shub M., Smale S. The Mathematics of Numerical Analysis. Lecture Notes in Appl. Math. 32:1996;895-914 Amer. Math. Soc. Providence.
25. Woźniakowski H. Tractability and strong tractability of linear multivariate problems. J. Complexity. 10:1994a;96-128.
26. Woźniakowski H. Tractability and strong tractability of multivariate tensor product problems. J. Comput. Information. 4:1994b;1-19.
27. Woźniakowski H. Efficiency of quasi-Monte Carlo algorithms for high dimensional integrals. Niederreiter H., Spanier J. Monte Carlo and Quasi-Monte Carlo Methods 1998. 1999;114-136 Springer-Verlag, Berlin.