Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4608609 | Journal of Complexity | 2014 | 17 Pages |
Abstract
We continue the complexity analysis of parametric definite and indefinite integration given by Daun and Heinrich (2013). Here we consider anisotropic classes of functions, including certain classes with dominating mixed derivatives. Our analysis is based on a multilevel Monte Carlo method developed by Daun and Heinrich (2013) and we obtain the order of the deterministic and randomized n-th minimal errors (in some limit cases up to logarithms). Furthermore, we compare the rates in the deterministic and randomized setting to assess the gain reached by randomization.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Thomas Daun, Stefan Heinrich,