## Abstract

We consider the problem of numerical integration for weighted anchored and ANOVA Sobolev spaces of s-variate functions. Here s is large including s=∞. Under the assumption of sufficiently fast decaying weights, we prove in a constructive way that such integrals can be approximated by quadratures for functions f_{k} with only k variables, where k=k(ε) depends solely on the error demand ε and is surprisingly small when s is sufficiently large relative to ε. This holds, in particular, for s=∞ and arbitrary ε since then k(ε)<∞ for all ε. Moreover k(ε) does not depend on the function being integrated, i.e., is the same for all functions from the unit ball of the space.

Original language | English |
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Pages (from-to) | 63-85 |

Number of pages | 23 |

Journal | Journal of Complexity |

Volume | 35 |

DOIs | |

State | Published - Aug 1 2016 |

### Bibliographical note

Funding Information:P. Kritzer is supported by the Austrian Science Fund (FWF): Project F5506-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”. F. Pillichshammer is partially supported by the Austrian Science Fund (FWF): Project F5509-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.

Publisher Copyright:

© 2016 Elsevier Inc.

## Keywords

- Numerical integration
- Truncation dimension
- Weighted anchored and ANOVA Sobolev spaces

## ASJC Scopus subject areas

- Algebra and Number Theory
- Statistics and Probability
- Numerical Analysis
- Mathematics (all)
- Control and Optimization
- Applied Mathematics