Variants of the Koksma-Hlawka inequality for vertex-modified quasi-Monte Carlo integration rules. (English) Zbl 0855.11040
Summary: Vertex-modified rules have recently been introduced by the authors as a way of improving the performance of quasi-Monte Carlo methods for numerical integration. In this paper, they establish variants of the Koksma-Hlawka inequality for vertex-modified rules, and show that there are choices for the vertex weights which, in general, yield smaller error bounds than the classical Koksma-Hlawka bound. Low-discrepancy point sets for which the local discrepancy has constant sign emerge as interesting objects of study.
MSC:
| 11K45 | Pseudo-random numbers; Monte Carlo methods |
| 65C05 | Monte Carlo methods |
| 65D30 | Numerical integration |
Keywords:
quasi-Monte Carlo methods for numerical integration; Koksma-Hlawka inequality for vertex-modified rules; discrepancyReferences:
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