abstract:
For analytic d-variate multivariate problems it is natural to expect an exponential convergence and complexity bounds as a function of d and 1 + log ε−1 , where ε is an error threshold. We study necessary and sufficient conditions on exponential convergence and uniform exponential convergence. The latter holds when the exponent of exponential convergence is independent of d. We also study necessary and sufficient conditions when complexity bounds are polynomial in d and 1 + log ε−1 , and when they are not exponential in d and 1 + log ε−1 .
The talk is based on joint papers with J. Dick, F. Kuo, P. Kritzer G. Larcher, F. Pillichshammer, and I. Sloan. |