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关于MIT 6.00课程lec06--牛顿法

发布于 2024-12-20 08:15:27 字数 843 浏览 1 评论 0原文

我尝试用自己的方式编码，但发现我得到了错误的答案。

我已阅读此页面。并尝试启动该过程：

在此处输入图像描述

f(x)=x^2-e

数学：

在此处输入图像描述

所以这是我的代码：

def sqrtRootNR(num, count, epsl):
    """
    for test
    """
    num = float(num)
    guess = num / 2.0
    diff = guess ** 2.0 - num
    _cnt = 0
    while abs(diff) > epsl and _cnt < count:
        guess = guess - (guess ** 2.0 + epsl) / (guess * 2.0)
        diff = guess ** 2.0 - num
        _cnt = _cnt +1
    print guess, _cnt

sqrtRootNR(2, 100, 0.0001)

但是，我得到了错误的答案。

该函数的输出是：

D:\poc>python sq.py
0.0595177826557 100

原文

I have tried to code in my own way, but found I got the wrong answer.

I have read this page. And try to start the process:

enter image description here

f(x)=x^2-e

The math:

enter image description here

So there is my code:

def sqrtRootNR(num, count, epsl):
    """
    for test
    """
    num = float(num)
    guess = num / 2.0
    diff = guess ** 2.0 - num
    _cnt = 0
    while abs(diff) > epsl and _cnt < count:
        guess = guess - (guess ** 2.0 + epsl) / (guess * 2.0)
        diff = guess ** 2.0 - num
        _cnt = _cnt +1
    print guess, _cnt

sqrtRootNR(2, 100, 0.0001)

However, I got the wrong answer.

The output of this function is:

D:\poc>python sq.py
0.0595177826557 100

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茶花眉 2024-12-27 08:15:27

编程的一项重要技能是知道哪些信息最有用。如果添加一些简单的调试信息：

while abs(diff) > epsl and _cnt < count:
    guess = guess - (guess ** 2.0 + epsl) / (guess * 2.0)
    diff = guess ** 2.0 - num
    print guess, _cnt
    _cnt = _cnt +1
print guess, _cnt

您可以看到您的程序很快就会出错：

$ ./sqrt.py 
0.49995 0
0.249874989999 1
0.124737394941 2
0.0619678553654 3
0.0301770577385 4
0.0134316410297 5
0.00299326718803 6
-0.0152075217183 7
-0.00431591416548 8
0.00942707405618 9
-0.000590335594744 10
....

每次迭代似乎都会将数字减半，直到变为负数，此时行为很难一眼看出。但你可以明显看出，最初的几次迭代是错误的。

对我来说看起来很可疑的东西：(guess ** 2.0 + epsl)

在评估牛顿平方根方法时，您实际上不应该使用 epsilon - 毕竟，您试图确保您的误差小于epsilon。

One important skill in programming is knowing which information where will be most useful. If you add some simple debugging information:

while abs(diff) > epsl and _cnt < count:
    guess = guess - (guess ** 2.0 + epsl) / (guess * 2.0)
    diff = guess ** 2.0 - num
    print guess, _cnt
    _cnt = _cnt +1
print guess, _cnt

You can see that your program goes wrong quickly:

$ ./sqrt.py 
0.49995 0
0.249874989999 1
0.124737394941 2
0.0619678553654 3
0.0301770577385 4
0.0134316410297 5
0.00299326718803 6
-0.0152075217183 7
-0.00431591416548 8
0.00942707405618 9
-0.000590335594744 10
....

It appears to halve the number every iteration until it goes negative, when the behavior gets very difficult to tell just at a glance. But you can obviously tell that the very first few iterations are wrong.

Something that looks quite fishy to me: (guess ** 2.0 + epsl)

You shouldn't actually use epsilon when evaluating Newton's method for square roots -- after all, you're trying to make sure your error is less than epsilon.

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