Abstract
Extensible integration lattices have the attractive property that the number of points in the node set may be increased while retaining the existing points. It is shown here that there exist generating vectors, h, for extensible rank-1 lattices such that for n = b, b2, ... points and dimensions s = 1, 2, ... the figures of merit Rα, Pα, and discrepancy are all small. The upper bounds obtained on these figures of merit for extensible lattices are some power of log n worse than the best upper bounds for lattices where h is allowed to vary with n and s.
Original language | English |
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Pages (from-to) | 286-300 |
Number of pages | 15 |
Journal | Journal of Complexity |
Volume | 19 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jun 2003 |
Externally published | Yes |
Scopus Subject Areas
- Algebra and Number Theory
- Statistics and Probability
- Numerical Analysis
- General Mathematics
- Control and Optimization
- Applied Mathematics
User-Defined Keywords
- Discrepancy
- Extensible lattices
- Figures of merit
- Lattice rules
- Quasi-Monte Carlo integration