I want to make a Python program that will run a bisection method to determine the root of:
f(x) = -26 + 85x - 91x2 +44x3 -8x4 + x5
The Bisection method is a numerical method for estimating the roots of a polynomial f(x).
Are there any available pseudocode, algorithms or libraries I could use to tell me the answer?
8 Answers
Basic Technique
Here's some code showing the basic technique:
>>> def samesign(a, b):
return a * b > 0
>>> def bisect(func, low, high):
'Find root of continuous function where f(low) and f(high) have opposite signs'
assert not samesign(func(low), func(high))
for i in range(54):
midpoint = (low + high) / 2.0
if samesign(func(low), func(midpoint)):
low = midpoint
else:
high = midpoint
return midpoint
>>> def f(x):
return -26 + 85*x - 91*x**2 +44*x**3 -8*x**4 + x**5
>>> x = bisect(f, 0, 1)
>>> print(x, f(x))
0.557025516287 3.74700270811e-16
