[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む25 [無断転載禁止]©2ch.net (716ﾚｽ)

現代数学の系譜11 ガロア理論を読む25 [無断転載禁止]©2ch.net http://rio2016.5ch.net/test/read.cgi/math/1477804000/

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521: 現代数学の系譜11 ガロア理論を読む [sage] 2016/11/27(日) 07:23:03.88 ID:dKz7cXDk >>519 関連 ＦＦＴ https://ja.wikipedia.org/wiki/%E9%AB%98%E9%80%9F%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B 高速フーリエ変換 (抜粋) 高速フーリエ変換（こうそくフーリエへんかん、英: Fast Fourier Transform、FFT）とは、離散フーリエ変換 (Discrete Fourier Transform、DFT) を計算機上で高速に計算するアルゴリズム。FFTの逆変換をIFFT (Inverse FFT) と呼ぶ。 歴史 高速フーリエ変換といえば一般的には1965年、ジェイムズ・クーリー（英語版） (J. W. Cooley) とジョン・テューキー (J. W. Tukey) が発見した[1]とされているCooley-Tukey型FFTアルゴリズム（英語版）を呼ぶ[2]。しかし、1805年ごろにガウスが同様のアルゴリズムを独自に発見していた[3]。 (引用終り) http://rio2016.5ch.net/test/read.cgi/math/1477804000/521

522: 現代数学の系譜11 ガロア理論を読む [sage] 2016/11/27(日) 07:24:02.85 ID:dKz7cXDk >>521 関連 英文版 ＦＦＴの歴史が詳しいね https://en.wikipedia.org/wiki/Fast_Fourier_transform (抜粋) History The development of fast algorithms for DFT can be traced to Gauss's unpublished work in 1805 when he needed it to interpolate the orbit of asteroids Pallas and Juno from sample observations.[5] His method was very similar to the one published in 1965 by Cooley and Tukey, who are generally credited for the invention of the modern generic FFT algorithm. While Gauss's work predated even Fourier's results in 1822, he did not analyze the computation time and eventually used other methods to achieve his goal. Between 1805 and 1965, some versions of FFT were published by other authors. Yates in 1932 published his version called interaction algorithm, which provided efficient computation of Hadamard and Walsh transforms.[6] Yates' algorithm is still used in the field of statistical design and analysis of experiments. In 1942, Danielson and Lanczos published their version to compute DFT for x-ray crystallography, a field where calculation of Fourier transforms presented a formidable bottleneck.[7] While many methods in the past had focused on reducing the constant factor for O ( n^2 ) computation by taking advantage of symmetries, Danielson and Lanczos realized that one could use the periodicity and apply a "doubling trick" to get O ( n log ? n ) runtime.[8] つづく http://rio2016.5ch.net/test/read.cgi/math/1477804000/522

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