Question

这是我使用while循环的牛顿方法的代码，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，以便可以通过测试与根之一的距离是否小于0.25来检查函数是否将收敛。

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收敛性。这种差异只是您在每次迭代中添加的值，即fz / dfz。

我猜您需要在差值小于0.25时停止循环，然后代码如下：

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

您还可以打印fz / dfz的值以检查其是否确实达到收敛

牛顿方法在python中检查

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