Secant Method Implementation in Python

secant.py

#!/usr/bin/python3.6

# This method is quite similar to that of the Regula-Falsi method except for the
# condition f(x1).f(x2) < 0. Here the graph of the function y = f(x) in the
# neighborhood of the root is approximated by a secant line or chords. Further,
# the interval at each iteration may not contain the root.
# Let the limits of interval initially be x0 and x1.

# Then the first approximation is given by:
#         x2 = x1 – [(x1-x0)/f(x1)-f(x0)]f(x1)
# Again, the formula for successive approximation in general form is
#         x(n+1) = xn - [xn - x(n-1)/f(xn)-f(x(n-1))]f(xn)

import math

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

def secant(a, b):
    while True:
        fa = f(a)
        fb = f(b)
        root = (a*fb-b*fa)/(fb-fa)

        tmp1 = round(b, 9)
        tmp2 = round(root, 9)
        if tmp1 == tmp2:
            print("The root of the given equation is %f"% root)
            return
        a = b
        b = root

a = float(input("Enter the first root: "))
b = float(input("Enter the second root: "))

secant(a, b)