第22章 数値演算

計算の目的は数値ではなく、洞察である。 R.W Hamming

しかし、学生にとっては数字は洞察にいたる最良の道であることが多い。 A.Ralston

wikipedia:Richard Hamming



まとめとして、私はすごいこともできるのに成功をつかめない人が非常に多い理由は以下の通りだと主張します。重大な問題に取り組まない、情熱的でない、難しい問題を重要さを損なわずにもっと簡単な問題に変えようとしない、仕事をしない言い訳を自分にし続ける。成功しない人は、それは運の問題だと言い続けます。私は運の問題だと言うのはどれくらい簡単かをみなさんに言いました。さらに私はみなさんに、心を入れ替える方法について述べました。ですから前に進んでください。そして偉大な科学者になってください! (終わり)

Mathematical Methods for Digital Computers
という名前の書物をあらわした人が、A・Ralston この人は、Wikipedia とかでは探すことができませんでした。

Richard Wesley Hamming (Chicago, February 11, 1915 – Monterey, California, January 7, 1998) was an American mathematician whose work had many implications for computer science and telecommunications. His contributions include the Hamming code (which makes use of a Hamming matrix), the Hamming window (described in Section 5.8 of his book Digital Filters), Hamming numbers, Sphere-packing (or hamming bound) and the Hamming distance.
He received his bachelor's degree from the University of Chicago in 1937, a master's degree from the University of Nebraska in 1939, and finally a Ph.D. from the University of Illinois at Urbana-Champaign in 1942. He was a professor at the University of Louisville during World War II, and left to work on the Manhattan Project in 1945, programming one of the earliest electronic digital computers to calculate the solution to equations provided by the project's physicists. The objective of the program was to discover if the detonation of an atomic bomb would ignite the atmosphere. The result of the computation was that this would not occur, and so the United States used the bomb, first in a test in New Mexico, and then twice against Japan.
Later, from 1946 to 1976, he worked at the Bell Telephone Laboratories, where he collaborated with Claude E. Shannon. During this period, he was an Adjunct Professor at the City College of New York, School of Engineering. On July 23, 1976 he moved to the Naval Postgraduate School, where he worked as an Adjunct Professor until 1997, when he became Professor Emeritus.
He was a founder and president of the Association for Computing Machinery. His philosophy on scientific computing appears as preface to his 1962 book on numerical methods:



22−1 イントロダクション

22−2 限界値

22−3 標準数学関数

22−4 ベクタ演算
 22−4−1 vararrayの構築
 22−4−2 vararrayの添え字操作と代入
 22−4−3 メンバ演算
 22−4−4 非メンバ演算
 22−4−5 slice
 22−4−6 slice-array
 22−4−7 一時オブジェクト コピー ループ
 22−4−8 汎用スライス
 22−4−9 mask
 22−4−10 indirect-array

22-5 複素数

22-6 汎用数学アルゴリズム
 22-6-1 accumulate
 22-6-2 inner_product
 22-6-3 差分的変化

22-7 乱数

22-8 アドバイス

22-9 練習問題