pt_fixe_lagrange.py

Created by alten01

Created on December 11, 2024

530 Bytes

methode de lagrange

methode pour approcher une sol de 
l eq f(x)=0

xn satisfait 
f(bn)-f(an)/bn-an*(xn-bn)+f(bn)=0
soit xn =
an*f(bn)-bn*f(an)/f(bn)-f(an)

on etudie le signe de f(xn)
Si f(xn)<0 on remplace an par xn
Si f(xn)>0 on remplace bn par xn

conditions dutilisation
f continue 
f(a)*f(b)<0
f doit etre convexe ou concave
=> f''>0 ou f''<0

criteres darret
- qd la valeur de la fct est 
proche de 0 :
abs(f(xn))<epsilon
- qd la diff entre les 2 iterations
est tres petite : 
abs(xn+1-xn)<epsilon

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