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Van der Corput Sequence: Low- Discrepancy Sequence, Unit Interval -

English
2026-03-17
€156.58 €195.73

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High Quality Content by WIKIPEDIA articles! 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 ... Full description

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High Quality Content by WIKIPEDIA articles! 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: frac{1}{2}, frac{1}{4}, frac{3}{4}, frac{1}{8}, frac{5}{8}, frac{3}{8}, frac{7}{8}, frac{1}{16}, frac{9}{16}, frac{5}{16}, frac{13}{16}, frac{3}{16}, frac{11}{16}, frac{7}{16}, frac{15}{16}, ldots The elements of the van der Corput sequence (in any base) form a dense set in the unit interval: for any real number in [0, 1] there exists a subsequence of the van der Corput sequence that converges towards that number. They are also uniformly distributed over the unit interval.

More Information

Publisher OmniScriptum
Release year 2026
Cover type Softcover
EAN 9786131122989
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€156.58 €195.73