import numpy as np
import matplotlib.pyplot as plt

#Computing negative eigenvalue of problem 8.46 by Newton's method.

def f(x):
    return np.tanh(x)-x/(2.-x*x)

def df(x):
    return 1./(np.cosh(x)**2)-(2.+x*x)/((2-x*x)**2)

eps = 0.0000001 #Tolerance
x = 1.3 #Initial value
n = 0 
print n,': ', x
while (np.abs(f(x)) >= eps and n < 50):
  x = x - f(x)/df(x) 
  n = n+1
  print n, ': ', x