國考計算機解數學題疊代

f (X) = X+2.4638 cos X
f '(X) = 1- 2.4638 sin X
希望 f(X) =2.5844

Step 1
Xo=0 , f(Xo) =f(0) = 0+2.4638 cos0 = 2.4638
f'(Xo) =f '(0) =1-2.4638 sin 0 = 1

f(X1) = f(Xo) + f '(Xo) (X1 -Xo)
=f(0) + f '(0) (X1 -0)
= 2.4638+1 ×X1
f(X1)=2.5844 => X1=0.1206


Step 2
X1 =0.1206 , f(X1) = 0.1206 +2.4638 cos0.1206 =2.566504509
f ' (X1) = 1-2.4638 sin0.1206 =0.703585467

f(X2) = f(X1) +f '(X1) (X2 -X1)
=2.566504509 +0.703585467 (X2 - 0.1206)
f(X2) =2.5844 => X2 = 0.14597703



Step 3
X2 = 0.14597703 ,f(X2) = 2.583572694
f '(X2) = 0.470492438

f(X3) = f(X2) +f '(X2) (X3-X2)
=2.583572694 +0.470492438 (X3- 0.14597703)
f(X3) =2.5844 => X3 = 0.147735402


Step 4
X3 = 0.147735402 ,f(X3) =2.584697129
( 2.584697129 - 2.5844)/ 2.5844 ×100% =0.01%
誤差0.01%夠小，可接受了

Ans : X =0.147735402


數學軟體求出Ｘ解為0.14727
https://www.wolframalpha.com/input/?i=X%2B2.4638COSX%EF%BC%9D2.5844




2014-11-18 21:45:14 補充：
功能太強大的 ， 國考不能用

用fx-911型吧～