Secant Method¶
In [1]:
import numpy as np
import matplotlib.pyplot as pt
%matplotlib inline
Here's a function: (Look here! No derivative.)
In [2]:
def f(x):
return x**3 - x +1
xmesh = np.linspace(-4, 4, 100)
pt.ylim([-3, 10])
pt.grid()
pt.plot(xmesh, f(xmesh))
Out[2]:
In [3]:
guesses = [2, 1.7]
Evaluate this cell many times in-place (using Ctrl-Enter)
In [13]:
# grab last two guesses
x = guesses[-1]
xbefore = guesses[-2]
slope = (f(x)-f(xbefore))/(x-xbefore)
# plot approximate function
pt.plot(xmesh, f(xmesh))
pt.plot(xmesh, f(x) + slope*(xmesh-x))
pt.plot(x, f(x), "o")
pt.plot(xbefore, f(xbefore), "o")
pt.ylim([-4, 4])
pt.ylim([-3, 10])
pt.axhline(0, color="black")
# Compute approximate root
xnew = x - f(x) / slope
guesses.append(xnew)
print(xnew)
In [ ]:
f(xnew)