A van der Corput sequence is a low-discrepancy sequence over the unit interval first published in 1935 by the Dutch mathematician J. G. van der Corput. It is constructed by reversing the base n representation of the sequence of natural numbers (1, 2, 3, …). For example, the decimal van der Corput sequence begins:
- 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.01, 0.11, 0.21, 0.31, 0.41, 0.51, 0.61, 0.71, 0.81, 0.91, 0.02, 0.12, 0.22, 0.32, …
whereas the binary van der Corput sequence can be written as:
- 0.12, 0.012, 0.112, 0.0012, 0.1012, 0.0112, 0.1112, 0.00012, 0.10012, 0.01012, 0.11012, 0.00112, 0.10112, 0.01112, 0.11112, …
or, equivalently, as:
The elements of the van der Corput sequence (in any base) form a dense set in the unit interval: for any real number in there exists a subsequence of the van der Corput sequence that converges towards that number. They are also equidistributed over the unit interval.
Famous quotes containing the words van, der and/or sequence:
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