如何在Python中执行Bisection方法

问题描述

我想制作一个Python程序，该程序将运行二分法来确定其根：

I want to make a Python program that will run a bisection method to determine the root of:

f(x) = -26 + 85x - 91x2 +44x3 -8x4 + x5

对分法是一种用于估计多项式f（x）的根。

The Bisection method is a numerical method for estimating the roots of a polynomial f(x).

有没有可用的伪代码，算法或库可以用来告诉我答案？

Are there any available pseudocode, algorithms or libraries I could use to tell me the answer?

推荐答案

以下代码显示了基本技术：

Here's some code showing the basic technique:

>>> 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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