Abstract
This chapter presents methods for estimating discrepancy and discusses discrepancy of sequences of real numbers. Because of the natural order in the real number system, the one-dimensional case allows for many results, which do not possess an analogue in several dimensions. The relations between discrepancy and numerical integration are intimate. Low discrepancy sequences are suitable for nodes in a numerical integration method. The sequence of fractional parts is uniformly distributed. For numbers α, which are badly approximable by rationals, for example, the irrationals α having bounded partial quotients in their continued fraction expansion, very sharp estimates for the discrepancy can be obtained by using the method of Ostrowski, which exploits properties of continued fractions.
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