1. CONSTRUCTING RANDOMLY SHIFTED LATTICE RULES IN WEIGHTED SOBOLEV SPACES.
- Author
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Sloan, I.H., Kuo, F.Y., and Joe, S.
- Subjects
- *
MONTE Carlo method , *MATHEMATICAL functions , *SOBOLEV spaces , *ERRORS , *INTEGRALS , *RESEARCH - Abstract
Shifted rank-1 lattice rules, a special class of quasi-Monte Carlo methods, have recently been proposed by the present authors for the integration of functions belonging to certain "weighted" Sobolev spaces. The shifts in these rules were generated in a deterministic manner. In contrast, in this paper we generate these shifts randomly. This allows probabilistic estimates for the error in a given integral. It also reduces the number of operations required to find the generating vectors for the underlying lattice rules component-by-component. The rules thus constructed achieve a worst-case strong tractability error bound in an average or probabilistic sense. [ABSTRACT FROM AUTHOR]
- Published
- 2002
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