Homework_2018_1_02_1032478036.ipynb

Kernel: Python 3

Fixed-point iteration

TAREA: Encontrar las tres raices de la función $f(x) = x^2\cos(2x)$ utilizando optimize.fixed_point

from scipy import optimize
%pylab inline
import matplotlib.pyplot as plt
import numpy as np

Populating the interactive namespace from numpy and matplotlib

/usr/local/lib/python3.4/dist-packages/IPython/core/magics/pylab.py:160: UserWarning: pylab import has clobbered these variables: ['f']
`%matplotlib` prevents importing * from pylab and numpy
  "\n`%matplotlib` prevents importing * from pylab and numpy"

#Gráfica de la funcion
x = np.linspace(-1,1,100)
plt.plot(x,x**2*np.cos(2*x))
plt.grid()

def f(x):
    return x**2*np.cos(2*x)
def g(x):
    return x-f(x)
root1=optimize.fixed_point(g,1)
root2=optimize.fixed_point(g,20)
root3=optimize.fixed_point(g,0.1)
print ('Algunas raíces de la función son: x={} , x={} y x={}'.format(root1,root2,root3))

Algunas raíces de la función son: x=0.7853981633974483 , x=-0.7853981633974483 y x=1.2787076310012914e-09