High-dimensional integration: The quasi-Monte Carlo way*†

@article{Dick2013HighdimensionalIT,
  title={High-dimensional integration: The quasi-Monte Carlo way*†},
  author={Josef Dick and Frances Y. Kuo and Ian H. Sloan},
  journal={Acta Numerica},
  year={2013},
  volume={22},
  pages={133 - 288}
}
This paper is a contemporary review of QMC (‘quasi-Monte Carlo’) methods, that is, equal-weight rules for the approximate evaluation of high-dimensional integrals over the unit cube [0,1]s, where s may be large, or even infinite. After a general introduction, the paper surveys recent developments in lattice methods, digital nets, and related themes. Among those recent developments are methods of construction of both lattices and digital nets, to yield QMC rules that have a prescribed rate of… Expand
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