## Abstract

We prove that for every dimension s and every number n of points, there exists a point-set P_{n,s} whose γ-weighted unanchored L _{∞} discrepancy is bounded from above by C(b)/n^{1/2-b} independently of s provided that the sequence γ = {γ_{k}} has ∑_{k=1}^{∞} γ_{k}^{a} for some (even arbitrarily large) a. Here 6 is a positive number that could be chosen arbitrarily close to zero and C(b) depends on b but not on s or n. This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals ∫_{D}f(x)ρ(x)dx over unbounded domains such as D = ℝ^{s}. It also supplements the results that provide an upper bound of the form C√s/n when γ_{k} ≡ 1.

Original language | English |
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Pages (from-to) | 1903-1911 |

Number of pages | 9 |

Journal | Mathematics of Computation |

Volume | 73 |

Issue number | 248 |

DOIs | |

State | Published - Oct 2004 |

## Keywords

- Low discrepancy points
- Tractability
- Weighted integration
- quasi-Monte Carlo methods

## ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics