TY - GEN

T1 - High-Discrepancy Sequences for High-Dimensional Numerical Integration

AU - Tezuka, Shu

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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).

AB - 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).

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U2 - 10.1007/978-3-642-27440-4_40

DO - 10.1007/978-3-642-27440-4_40

M3 - Conference contribution

AN - SCOPUS:84893606322

SN - 9783642274398

T3 - Springer Proceedings in Mathematics and Statistics

SP - 685

EP - 694

BT - Monte Carlo and Quasi-Monte Carlo Methods 2010

PB - Springer New York LLC

T2 - 9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010

Y2 - 15 August 2010 through 20 August 2010

ER -