@inproceedings{bfcbb78c09b44c029a5b1e0bd89f76e6,
title = "Van der Corput and golden ratio sequences along the hilbert space-filling curve",
abstract = "This work investigates the star discrepancies and squared integration errors of two quasi-random points constructions using a generator one-dimensional sequence and the Hilbert space-filling curve. This recursive fractal is proven tomaxi-mize locality and passes uniquely through all points of the d-dimensional space. The van der Corput and the golden ratio generator sequences are compared for randomized integro-approximations of both Lipschitz continuous and piecewise constant functions. We found that the star discrepancy of the construction using the van der Corput sequence reaches the theoretical optimal rate when the number of samples is a power of two while using the golden ratio sequence performs optimally for Fibonacci numbers. Since the Fibonacci sequence increases at a slower rate than the exponential in base 2, the golden ratio sequence is preferable when the budget of samples is not known beforehand. Numerical experiments confirm this observation.",
keywords = "Discrepancy, Golden ratio sequence, Hilbert curve, Numerical integration, Quasi-random points",
author = "Colas Schretter and Zhijian He and Mathieu Gerber and Nicolas Chopin and Harald Niederreiter",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; 11th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2014 ; Conference date: 06-04-2014 Through 11-04-2014",
year = "2016",
month = jan,
day = "1",
doi = "10.1007/978-3-319-33507-0\_28",
language = "English",
isbn = "9783319335056",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "531--544",
editor = "Ronald Cools and Dirk Nuyens",
booktitle = "Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2014",
}