Copyright (C) 2020 Andreas Kloeckner
MIT LicensePermission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
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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)