Finite-order weights imply tractability of linear multivariate problems

Journal of Approximation Theory

Volumn 130, Issue 1, 2004, Pages 57-77

  Wasilkowski, Greg W ^a   Wozniakowski H ^b,c  

^a UNIVERSITY OF KENTUCKY   (United States)

^b Columbia University ^*  (United States)

^c UNIVERSITY OF WARSAW   (Poland)

Author keywords

Approximation; Integration; Multivariate problems; Tractability

Indexed keywords

EID: 11144293601     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jat.2004.06.011     Document Type: Article

References (21)

1. N. Aronszajn Theory of reproducing kernels Trans. Amer. Math. Soc. 68 1950 337-404
2. R.E. Caflisch W. Morokoff A. Owen Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension J. Comput. Finance 1 1997 27-46
3. J. Dick, I.H. Sloan, X. Wang, H. Woźniakowski, Good lattice rules in weighted Korobov spaces with general weights, 2003, submitted for publication.
4. F.Y. Kuo, I.H. Sloan, Quasi-Monte Carlo methods can be efficient for integration over products of spheres, 2003, submitted for publication.
5. M. Kwas, Complexity of multivariate Feynman-Kac path integration in randomized and quantum settings, in preparation.
6. M. Kwas Y. Li Worst case complexity of multivariate Feynman-Kac path integration J. Complexity 19 2003 730-743
7. E. Novak H. Woźniakowski When are integration and discrepancy tractable? In: R.A. DeVore A. Iserlis E. Süli (Eds.) FOCM Proceedings of Oxford 1999 2001 Cambridge University Press Cambridge 211-266
8. E. Novak H. Woźniakowski Intractability results for integration and discrepancy J. Complexity 17 2001 388-441
9. I.H. Sloan X. Wang H. Woźniakowski Finite-order weights imply tractability of multivariate integration J. Complexity 20 2004 46-74
10. I.H. Sloan H. Woźniakowski When are Quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complexity 14 1998 1-33
11. J.F. Traub G.W. Wasilkowski H. Woźniakowski Information-based Complexity 1988 Academic Press New York
12. J.F. Traub A.G. Werschulz Complexity and Information 1998 Cambridge University Press Cambridge
13. J.F. Traub H. Woźniakowski A General Theory of Optimal Algorithms 1980 Academic Press New York
14. X. Wang K.T. Fang Effective dimensions and quasi-Monte Carlo integration J. Complexity 19 2003 101-124
15. X. Wang, I.H. Sloan, Why are high-dimensional finance problems often of low effective dimension?, 2003, submitted for publication.
16. G.W. Wasilkowski H. Woźniakowski Weighted tensor-product algorithms for linear multivariate problems J. Complexity 15 1999 402-447
17. G.W. Wasilkowski H. Woźniakowski On the power of standard information for weighted approximation Found. Comput. Math. 1 2001 417-434
18. G.W. Wasilkowski H. Woźniakowski Tractability of approximation and integration for weighted tensor product problems over unbounded domains In: K.-T. Fang F.J. Hickernell H. Niederreiter (Eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000 2002 Springer Berlin 497-522
19. G.W. Wasilkowski, H. Woźniakowski, Polynomial-time algorithms for linear multivariate problems with finite-order weights, in preparation.
20. H. Woźniakowski Tractability and strong tractability of linear multivariate problems J. Complexity 10 1994 96-128
21. 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 1999 Springer Berlin 114-136