Average case complexity of linear multivariate problems II. Applications

H Wogniakowski
1992 Journal of Complexity  
We apply the theoretical results of Part I (H. Woiniakowski, 1992, J. Complexity 8, in press) to linear multivariate problems LMP equipped with the folded Wiener sheet measure. We are particularly interested in multivariate weighted integration and multivariate function approximation. We prove that any LMP which satisfies (A. 1) of Part I is tractable and its exponent is at most 2. We show that optimal or nearly optimal sample points can be derived from hyperbolic cross points, and exhibit
more » ... y optimal algorithms. In particular, we find the order of the average case complexity of multivariate function approximation in AStd.
doi:10.1016/0885-064x(92)90002-s fatcat:5ti43kh2sveljmm6pjobmrhism