Secant Method

Copyright (C) 2020 Andreas Kloeckner

MIT License

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import numpy as np
import matplotlib.pyplot as pt

Here's a function: (Look here! No derivative.)

def f(x):
    return x**3 - x +1

xmesh = np.linspace(-2, 2, 100)
pt.ylim([-3, 10])
pt.grid()
pt.plot(xmesh, f(xmesh))

[<matplotlib.lines.Line2D at 0x7fc4f5a2c470>]

guesses = [2, 1.5]

Evaluate this cell many times in-place (using Ctrl-Enter)

# 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([-3, 10])
pt.axhline(0, color="black")

# Compute approximate root
xnew = x - f(x) / slope
guesses.append(xnew)
print(xnew)

-1.3247179572447458