获得epsilon的准确性

Question

我试图创建一个找到数字平方根的函数，而不使用平方根命令。这得到了没有任何库的epsilon准确性的答案，我现在有了基本代码

def mySqrt(b, e) :
    sqrt = b**.5

我尝试了很多不同的方法，但我无法弄清楚如何在epsilon中实现e

Answer 1

您可以实现Newton's method，这是一种迭代方法，可以将许多方程解算为任意精度。应用于平方根，递归为

或在Python代码中：

def my_sqrt(a, e):
    diff = e + 1  # random diff > e
    sqrt = 1.0  # start must not be 0
    while diff > e:
        sqrt = sqrt - (sqrt * sqrt - a) / (2 * sqrt)
        diff = sqrt * sqrt - a
        if diff < 0:  # make sure diff is positive without calling abs
            diff = -1 * diff 
    return sqrt

>>> my_sqrt(2, 0.00001)
1.4142156862745099

承认，这需要在重新考虑后考虑epsilon。因此，结果实际上比在epsilon中获取根本身更精确。

Answer 2

使用babylonian method查找平方根。至于准确性检查，您需要标准的sqrt函数，然后将(expected-outcome)/expected计算为百分比误差。