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Van Der Corput Sequence

Definition

Van der Corput sequences are a means of generating sequences of points that are maximally self-avoiding (a.k.a. quasirandom sequences). In the one-dimensional case, the simplest approach to generate such a sequence is to simply divide the interval into a number of equal subintervals. Similarly, one can divide an n-dimensional volume by uniformly partitioning each of its dimensions. However, these approaches, have a number of drawbacks for numerical integration, especially for high dimensions. Like quasirandom sequences, "permuted" van der Corput sequences are constrained by a low-discrepancy requirement, which has the net effect of generating points in a highly correlated manner (i.e., the next point "knows" where the previous points are).

Related term

quasirandom sequence

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