Newton Raphson method Implementation in Python

newton_raphson.py

#!/usr/bin/python3.6

# This method is generally used to improve the result obtained by one of the
# previous methods. Let x0 be an approximate root of f(x) = 0 and let x1 = x0 + h be
# the correct root so that f(x1) = 0.
# Expanding f(x0 + h) by Taylor’s series, we get
#          f(x0) + hf′(x0) + h2/2! f′′(x0) + ...... = 0
# Since h is small, neglecting h2 and higher powers of h, we get
#          f(x0) + hf′(x0) = 0 or h = – f(x0)/f'(x0)
# A better approximation than x0 is therefore given by x1, where
#          x1 = x0 - f(x0)/f'(x0)
# Successive approximations are given by x2, x3, ....... , xn + 1, where
#          x(n+1) = xn - f(xn)/f'(xn)             (n = 0, 1, 2, 3, .......)
# Which is Newton-Raphson formula.

def f(x):
    fx = 3*x**2-15*x+7
    return fx

def fd(x):
    fdx = 6*x-15
    return fdx

def newton(guess):
    i = 0
    while True:
        root = guess - (f(guess)/fd(guess))
        print(f"Root after iteration {i+1} is {root}.")
        tmp1 = round(guess, 9)
        tmp2 = round(root, 9)

        if tmp1 == tmp2:
            return root
        guess = root
        i = i + 1

guess = float(input("Enter the guess value: "))
root = newton(guess)
print(f"The final root is {root}")