Discrepancy and Uniformity
نویسنده
چکیده
It can be proved that 1/N ≤ DN ≤ 1 and 1/(2N) ≤ D∗ N ≤ DN ≤ 2D∗ N . The sequence X is uniformly distributed in [0, 1) if and only if limN→∞DN(X) = 0. We are interested in low-discrepancy sequences, that is, sequences X for which DN(X) is small for all N . The efficient construction of such X is essential in quasi-Monte Carlo algorithms used, for example, to approximate a multivariate integral or to simulate certain random processes [1, 2, 3]. On the one hand, Béjian [4, 5] showed that
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