Abstract
We study discrepancy with arbitrary weights in the L2 norm over the d-dimensional unit cube. The exponent p* of discrepancy is defined as the smallest p for which there exists a positive number K such that for all d and all ε ≤ 1 there exist Kε-p points with discrepancy at most ε. It is well known that p* ∈ (1, 2]. We improve the upper bound by showing that p* ≤ 1.4778842. This is done by using; relations between discrepancy and integration in the average case setting with the Wiener sheet measure. Our proof is not constructive. The known constructive bound on the exponent p* is 2.454.
Original language | English |
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Pages (from-to) | 1125-1132 |
Number of pages | 8 |
Journal | Mathematics of Computation |
Volume | 66 |
Issue number | 219 |
DOIs | |
State | Published - Jul 1997 |
Keywords
- Average case
- Discrepancy
- Multivariate integration
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics