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解説しよう

ネタ元は「√でしまる」 インスパイア元は「ぽちっとな

ニュートン法:

「f(x) = 0 の近似解を X とすると、
 X - f(X)/f'(X) はより正確な近似解となる。」


f(x) = 0 の近似解 X から上につーっと線を伸ばすとf(X)に突き当ります。
その点からfの接線を引いたときのx軸との交点: X-Δは真値により近づきますな。

さて、接線の傾きはf'(X)であり、さらに上図の直角三角形の傾き f(X)/
Δ 一致します。
つまり  f'(X) = f(X)/Δ なんだから Δ = f(X)/f'(X)

したがってより近い近似値 X-Δ は X - f(X)/f'(X) となるっちゅースンポーです。

試験にでるよー 書いときな書いときなー

[追記] 近似値Xが真値より小さかったら X-f(X)/f'(X) は余計外れるんちゃうのん?
→ かもねー。んだけど一回その操作を施せば X > 真値 になるから...

投稿日時 : 2007年6月29日 21:42

コメントを追加

# re: 解説しよう 2007/06/29 22:33 Chuki

ナレーターの人ありがとう^^
ぽちっとな

# re: 解説しよう 2007/06/30 11:47 とりこびと

なんということでしょう!

先ほどまで記憶の彼方だったニュートン法がすっきりと頭に入ってくるではありませんか。

びふぉ~あふたぁ~。

# 『 The 祭り 』電卓アプリケーションをつくろう! 記事一覧 2007/07/08 11:23 AQUA's .NET 奮闘記

『 The 祭り 』電卓アプリケーションをつくろう! 記事一覧

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