Approximation of infinitely differentiable multivariate functions is intractable

Journal of Complexity

Volumn 25, Issue 4, 2009, Pages 398-404

  Novak, Erich ^a   Woźniakowski, Henryk ^b,c  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b Columbia University ^*  (United States)

^c UNIVERSITY OF WARSAW   (Poland)

Author keywords

Approximation of smooth functions; Curse of dimensionality; Rate of convergence; Tractability

Indexed keywords

COMPUTATIONAL COMPLEXITY; NUMERICAL ANALYSIS;

CURSE OF DIMENSIONALITY; LINEAR FUNCTIONALS; MULTIVARIATE FUNCTION; RATE OF CONVERGENCE; SMOOTH FUNCTIONS; TRACTABILITY; WORST CASE ERROR;

APPROXIMATION THEORY;

EID: 67649103535     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2008.11.002     Document Type: Article

References (8)

1. Novak E., and Woźniakowski H. Tractability of Multivariate Problems, Volume 1, Linear Information (2008), European Math. Soc, Zürich
2. Huang F.L., and Zhang S. Approximation of infinitely differentiable multivariate functions is not strongly tractable. J. Complexity 23 (2007) 73-81
3. A.G. Werschulz, H. Woźniakowski, Tractability of multivariate approximation over a weighted unanchored Sobolev space, Constr. Approx. (in press)
4. E. Novak, H. Woźniakowski, Optimal order of convergence and (in)tractability of multivariate approximation of smooth functions, Constr. Approx. (in press)
5. Sloan I.H., and Woźniakowski H. An intractability result for multiple integration. Math. Comp. 66 (1997) 1119-1124
6. Woźniakowski H. Open problems for tractability of multivariate integration. J. Complexity 19 (2003) 434-444
7. d) is not strongly tractable. J. Complexity 19 (2003) 638-643
8. E. Novak, Is there a curse of dimension for integration?, in: Choi-Hong Lai et al. (Eds.), 11th Int. Conf. on Domain Decomposition Methods DDM. org, Augsburg, London, 1998, pp. 89-96