CODEWITHSUNDEEP
pythonpython-3.xalgorithm
Wizard
Wizard

Reputation: 22103

find a cube root with Newton's method

Newton's method is to find successively better approximations to the roots of polynominal.
I have learned to find square root like:

    from sys import argv
    script, k,epsilon  = argv

    def find_square_root(k, epsilon):
        guess = k/2
        while abs(guess**2 -k) >= epsilon:
            guess = guess - (guess**2 -k)/(2*guess)
            print(f"Square root of {k} is about {guess}.")

    k = float(argv[1])
    epsilion = float(argv[2])
    find_square_root(k, epsilion)

Run it and come by:

    $ python3 successive_approximation.py 128 0.001
    Square root of 128.0 is about 33.0.
    Square root of 128.0 is about 18.439393939393938.
    Square root of 128.0 is about 12.690526879310774.Square root of 128.0 is about 11.388395266147043.
    Square root of 128.0 is about 11.31395340237364.
    Square root of 128.0 is about 11.313708501635368.

How to find a cube root with Newton's method?

Upvotes: 3

Views: 3177

Answers (1)

user3483203
user3483203

Reputation: 51155

Following this link:

def find_cube_root(k, epsilon):
  guess = k
  while(((1/3)*(2*guess + k/guess**2))**3 - k >= epsilon):
    guess = (1/3)*(2*guess + k/guess**2)
    print(f"Cube root of {k} is about {guess}.")

find_cube_root(100, .001)

Output:

Cube root of 100 is about 66.66999999999999.
Cube root of 100 is about 44.4541659167229.
Cube root of 100 is about 29.65297823132699.
Cube root of 100 is about 19.806561134963502.
Cube root of 100 is about 13.28934310575367.
Cube root of 100 is about 9.048305445603736.
Cube root of 100 is about 6.4393440686740675.
Cube root of 100 is about 5.096783929887992.
Cube root of 100 is about 4.6810321649028035.
Cube root of 100 is about 4.641920257658932.

Upvotes: 1

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