PYTHON CODE: Consider the equation X 4 = X 3 +10. [a,b]= [2,3] 33 steps of the B

Question

PYTHON CODE:

Consider the equation X4= X3+10.

[a,b]= [2,3]

33 steps of the Bisection method are requiired to calculate the solution within 10-10.

Write a PYTHON code to implement the Bisection method to find the solution. Use a for loop.

Explanation / Answer

>>> 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

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