Newton's Method
In [85]:
import numpy as np
import matplotlib.pyplot as pt
Here's a function:
In [86]:
def f(x):
return x**3 - x +1
def df(x):
return 3*x**2 - 1
xmesh = np.linspace(-2, 2, 100)
pt.ylim([-3, 10])
pt.plot(xmesh, f(xmesh))
Out[86]:
In [87]:
guesses = [2]
Evaluate this cell many times in-place (using Ctrl-Enter)
In [84]:
x = guesses[-1] # grab last guess
slope = df(x)
# plot approximate function
pt.plot(xmesh, f(xmesh))
pt.plot(xmesh, f(x) + slope*(xmesh-x))
pt.plot(x, f(x), "o")
pt.ylim([-3, 10])
pt.axhline(0, color="black")
# Compute approximate root
xnew = x - f(x) / slope
guesses.append(xnew)
print(xnew)
