牛顿法检查 python

Question

所以这是我使用 while 循环的牛顿法代码，z 是一个复杂的参数：

def which_root_z4(z , n): # function which takes 2 arguments; z and n
    fz = z ** 4 - 1 # defining f(z)
    dfz = 4 * z ** 3 # defining the first derivative of f(z)
    while n > 0:    # this block will continue looping until n = 0
        z = z - fz / dfz #T he Newton-Raphson formula
        return which_root_z4(z, n-1) # after each iteration, the function begins again with the new value of z and n-1
    return z

我需要对其进行修改，使其可以检查函数是否会收敛，方法是测试到其中一个根的距离是否小于 0.25。

我不知道该怎么做

方程的根是 1, -1 , i , i

谢谢

Answer 1

您可以通过查看 z 的当前值与其先前值之间的差异来检查是否收敛。这种差异只是您在每次迭代时添加的值，即 fz / dfz。

我猜你需要在差值小于0.25时停止循环，那么代码如下：

def which_root_z4(z , n):  # function which takes 2 arguments; z and n
fz = z ** 4 - 1 # defining f(z)
dfz = 4 * z ** 3 # defining the first derivative of f(z)
while n > 0:    # this block will continue looping until n = 0
    z = z - fz / dfz #T he Newton-Raphson formula

    if abs(fz / dfz)<0.25:  #This ends the loop when z's converged
        break

    return which_root_z4(z, n-1)  # after each iteration, the function begins again with the new value of z and n-1
return z

你也可以打印fz/dfz的值来检查它是否确实达到了收敛

牛顿法检查 python

Newton's method check in python

python

while-loop

newtons-method