In [3]:

    

import numpy as np

f = lambda x: x**2 - 25
fprime = lambda x: 2*x

MAX_STEPS = 100
TOLERANCE = 1e-4

xk = 0.06

for n in xrange(1, MAX_STEPS+1):
    xk = xk - (f(xk)/fprime(xk)) 
    print 'iteration xk =', xk
print 'xk = ', xk
print 'f(xk) = ', f(xk)


    

    




iteration xk = 208.363333333
iteration xk = 104.241658028
iteration xk = 52.2407426861
iteration xk = 26.3596481863
iteration xk = 13.6540337606
iteration xk = 7.74249725914
iteration xk = 5.48571481298
iteration xk = 5.02150302081
iteration xk = 5.00004603999
iteration xk = 5.00000000021
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
iteration xk = 5.0
xk =  5.0
f(xk) =  0.0