methode_de_newton.py

Created by alten01

Created on December 11, 2024

370 Bytes

- On cherche xbarre tq 
xbarre=g(xbarre)

On a f(x)=x^2-2
soit f'(x)=2x
On choisit un x0 astucieusement
On applique xn+1=xn-f(xn)/f'(xn)
xn+1 va ainsi tendre vers xbarre

- On veut mq xn+1 converge vers 
xbarre

On a xn+1=g(xn)
On derive g(x)
Soit g'(x) = 
1 -(f'(x))^2-f(x)f''(x)
/(f'(x))^2
= 1 - 1 = 0 <1

Donc xn+1 converge bien vers 
xbarre

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