### Abstract

In this paper, we consider a sequence of points in [0, 1]^{d}, which are distributed only on the diagonal line between (0,...,0) and (1,...,1). The sequence is constructed based on a one-dimensional low-discrepancy sequence. We apply such sequences to d-dimensional numerical integration for two classes of integrals. The first class includes isotropic integrals. Under a certain condition, we prove that the integration error for this class is O(√logN/N), where N is the number of points. The second class is called as Kolmogorov superposition integrals for which, under a certain condition, we prove that the integration error for this class is O((logN)/N).

Original language | English |
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Title of host publication | Monte Carlo and Quasi-Monte Carlo Methods 2010 |

Publisher | Springer New York LLC |

Pages | 685-694 |

Number of pages | 10 |

ISBN (Print) | 9783642274398 |

DOIs | |

Publication status | Published - Jan 1 2012 |

Event | 9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 - Warsaw, Poland Duration: Aug 15 2010 → Aug 20 2010 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 23 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | 9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 |
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Country | Poland |

City | Warsaw |

Period | 8/15/10 → 8/20/10 |

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### Cite this

*Monte Carlo and Quasi-Monte Carlo Methods 2010*(pp. 685-694). (Springer Proceedings in Mathematics and Statistics; Vol. 23). Springer New York LLC. https://doi.org/10.1007/978-3-642-27440-4_40