二分法求函式根

import math


def bisection(function, a, b):  # finds where the function becomes 0 in [a,b] using bolzano

    start = a
    end = b
    if function(a) == 0:  # one of the a or b is a root for the function
        return a
    elif function(b) == 0:
        return b
    elif function(a) * function(b) > 0:  # if none of these are root and they are both positive or negative,
        # then his algorithm can't find the root
        print("couldn't find root in [a,b]")
        return
    else:
        mid = (start + end) / 2
        while abs(start - mid) > 0.0000001:  # until we achieve precise equals to 10^-7
            if function(mid) == 0:
                return mid
            elif function(mid) * function(start) < 0:
                end = mid
            else:
                start = mid
            mid = (start + end) / 2
        return mid


def f(x):
    return math.pow(x, 3) - 2*x - 5


print(bisection(f, 1, 1000))
 

逐次逼近法

import math

def intersection(function,x0,x1): #function is the f we want to find its root and x0 and x1 are two random starting points
    x_n = x0
    x_n1 = x1
    while True:
        x_n2 = x_n1-(function(x_n1)/((function(x_n1)-function(x_n))/(x_n1-x_n)))
        if abs(x_n2 - x_n1)<0.00001 :
            return x_n2
        x_n=x_n1
        x_n1=x_n2

def f(x):
    return math.pow(x,3)-2*x-5

print(intersection(f,3,3.5))