Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces

作者：Ian H. Sloan, Frances Y. Kuo, Stephen Joe · 发表于：SIAM Journal on Numerical Analysis · 年份：2002 · DOI：10.1137/s0036142901393942 · 被引用次数：138 · 研究领域：Mathematical Approximation and Integration、Probabilistic and Robust Engineering Design、Statistical Methods and Inference

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.