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Ian Sloan and Lattice Rules

  • Peter KritzerEmail author
  • Harald Niederreiter
  • Friedrich Pillichshammer
Chapter

Abstract

Lattice rules are a powerful and popular form of quasi-Monte Carlo rules that are based on integration lattices. The study of the theory and application of lattice rules is intimately connected with the name Ian H. Sloan. We take the opportunity of Ian’s 80th birthday to give an overview of his wide-ranging and fruitful contributions to this topic.

Notes

Acknowledgements

The authors would like to thank two anonymous referees for their helpful remarks.

P. Kritzer is supported by the Austrian Science Fund (FWF) Project F5506-N26 and F. Pillichshammer by the Austrian Science Fund (FWF) Project F5509-N26. Both projects are parts of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Peter Kritzer
    • 1
    Email author
  • Harald Niederreiter
    • 1
  • Friedrich Pillichshammer
    • 2
  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria
  2. 2.Department of Financial Mathematics and Applied Number TheoryJohannes Kepler University LinzLinzAustria

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