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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Van der Corput sequence ： ウィキペディア英語版 Van der Corput sequence A van der Corput sequence is an example of the simplest one-dimensional low-discrepancy sequence over the unit interval; it was first described 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, …). The ''b''-ary representation of the positive integer ''n'' (≥ 1) is :$$ n=\sum_^d_k(n)b^k, where ''b'' is the base of in which number ''n'' is represented, and 0 ≤ ''d''k(''n'') < ''b'', i.e. the ''k''th digit in the ''b''-ary expansion of ''n''. The ''n''th number in the van der Corput sequence is $$ g_b(n)=\sum_^d_k(n)b^. == Examples == 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 is :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, :$\backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash tfrac,\; \backslash ldots.$ The elements of the van der Corput sequence (in any base) form a dense set in the unit interval; that is, for any real number in (1 ), there exists a subsequence of the van der Corput sequence that converges to that number. They are also equidistributed over the unit interval. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Van der Corput sequence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.