二分法 Jupyter Notebook

Question

使用二分法求 f(x) = sqrt(x) - cos(x) 的 p3，我在纸上得到了正确答案 p3 = .625

我在转换问题并使用 Jupyter notebook 解决问题时遇到了问题。有什么建议吗？

Jupyter Notebook code

Answer 1

0.625是近似过程中的第三次猜测，所以for循环应该在第四次迭代之前完成，代码如下。

import math

##problem statement
#finding a root of f(x) = sqrt(x)-cos(x) between the interval [0,1]
#f(0) = -1 f(1) = 0.45969..  so there is at least one root between the interval [0,1]

a = 0
b = 1
maxIt = 100
negative_result = math.sqrt(a) - math.cos(a)
positive_result = math.sqrt(b) - math.cos(b)

for i in range(maxIt):
    if i == 3:
        print("answer is: ", guess)
        break
    guess = (a+b)/2
    guess_result = math.sqrt(guess) - math.cos(guess)
    if guess_result*negative_result >= 0:
       a = guess
    else: 
        b = guess

输出为

0.625

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