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13 - Quasi-Monte Carlo Integration

from Part Two - Optimal Recovery

Published online by Cambridge University Press:  21 April 2022

Simon Foucart
Affiliation:
Texas A & M University
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Summary

This chapter is concerned with quasi-Monte Carlo rules, i.e., multivariate quadrature rules featuring equal weights and deterministically chosen evaluation points. The variation of a function and the star discrepancy of a set of points are defined as a prerequisite to the Koksma--Hlawka inequality, which bounds the error of a quasi-Monte Carlo rule by the product of the variation and the star discrepancy. Finally, some evaluation points with small star discrepancy are uncovered, namely the Halton sequence and the Hammersley set.

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Publisher: Cambridge University Press
Print publication year: 2022

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  • Quasi-Monte Carlo Integration
  • Simon Foucart, Texas A & M University
  • Book: Mathematical Pictures at a Data Science Exhibition
  • Online publication: 21 April 2022
  • Chapter DOI: https://doi.org/10.1017/9781009003933.019
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  • Quasi-Monte Carlo Integration
  • Simon Foucart, Texas A & M University
  • Book: Mathematical Pictures at a Data Science Exhibition
  • Online publication: 21 April 2022
  • Chapter DOI: https://doi.org/10.1017/9781009003933.019
Available formats
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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Quasi-Monte Carlo Integration
  • Simon Foucart, Texas A & M University
  • Book: Mathematical Pictures at a Data Science Exhibition
  • Online publication: 21 April 2022
  • Chapter DOI: https://doi.org/10.1017/9781009003933.019
Available formats
×