On the power of standard information for multivariate approximation in the worst case setting

Journal of Approximation Theory

Volumn 158, Issue 1, 2009, Pages 97-125

  Kuo, Frances Y ^a   Wasilkowski, Grzegorz W ^b   Woźniakowski, Henryk ^c,d  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF KENTUCKY   (United States)

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

^d UNIVERSITY OF WARSAW   (Poland)

Author keywords

Multivariate approximation; Standard information; Tractability; Worst case setting

Indexed keywords

EID: 64049103619     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2008.01.011     Document Type: Article

References (22)

1. Aronszajn N. Theory of reproducing kernels. Trans. AMS 68 (1950) 337-404
2. Hickernell F.J., Wasilkowski G.W., and Woźniakowski H. Tractability of linear multivariate problems in the average case setting. In: Keller A., Heinrich S., and Niederreiter H. (Eds). Monte Carlo and Quasi-Monte Carlo Methods 2006 (2008), Springer, Berlin 461-494
3. Hickernell F.J., and Woźniakowski H. Integration and approximation in arbitrary dimensions. Adv. Comput. Math. 12 (2000) 25-58
4. 2-approximation. J. Approx. Theory 153 (2008) 97-107
5. Kuo F.Y., Sloan I.H., and Woźniakowski H. Lattice rules for multivariate approximation in the worst case setting. In: Niederreiter H., and Talay D. (Eds). Monte Carlo and Quasi-Monte Carlo Methods 2004 (2006), Springer 289-330
6. Kuo F.Y., Sloan I.H., and Woźniakowski H. Lattice rule algorithms for multivariate approximation in the average case setting. J. Complexity 24 (2008) 283-323
7. ∞ approximation in the worst case setting over reproducing kernel Hilbert spaces. J. Approx. Theory 152 (2008) 135-160
8. Li Y. Applicability of Smolyak's algorithm to certain Banach spaces of multivariate functions. J. Complexity 18 (2002) 792-814
9. Novak E. Deterministic and Stochastic Error Bounds in Numerical Analysis. Lect. Notes in Math. vol. 1349 (1988), Springer-Verlag, Berlin
10. Novak E., Sloan I.H., and Woźniakowski H. Tractability of approximation for weighted Korobov spaces on classical and quantum computers. Found. Comput. Math. 4 (2004) 121-156
11. Papageorgiou A., and Wasilkowski G.W. On the average complexity of multivariate problems. J. Complexity 6 (1990) 1-23
12. Plaskota L. Noisy Information and Computational Complexity (1996), Cambridge Univ. Press, Cambridge
13. Ritter K. Average-Case Analysis of Numerical Problems. Lect. Notes in Math. vol. 1733 (2000), Springer-Verlag, Berlin
14. Traub J.F., Wasilkowski G.W., and Woźniakowski H. Information-Based Complexity (1988), Academic Press, New York
15. Traub J.F., and Werschulz A.G. Complexity and Information (1998), Cambridge Univ. Press, Cambridge
16. Traub J.F., and Woźniakowski H. A General Theory of Optimal Algorithms (1980), Academic Press, New York
17. G. Wahba, Spline Models for Observational Data, CBMS-NSF 59, Philadelphia, 1990
18. Wasilkowski G.W., and Woźniakowski H. Explicit cost bounds of algorithms for multivariate tensor product problems. J. Complexity 11 (1995) 1-56
19. Wasilkowski G.W., and Woźniakowski H. Weighted tensor product algorithms for linear multivariate problems. J. Complexity 15 (1999) 402-447
20. Wasilkowski G.W., and Woźniakowski H. On the power of standard information for weighted approximation. Found. Comput. Math. 1 (2001) 417-434
21. Wasilkowski G.W., and Woźniakowski H. Tractability of approximation and integration for weighted tensor product problems over unbounded domains. In: Fang K.-T., Hickernell F.J., and Niederreiter H. (Eds). Monte Carlo and Quasi-Monte Carlo Methods 2000 (2002), Springer 497-522
22. Werschulz A.G. The Computational Complexity of Differential and Integral Equations (1991), Oxford Univ. Press, Oxford