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def newton_method ( f , f_prime , x0 , tol = 1e-6 , max_iter = 100 ) :
"""
牛顿迭代法计算函数值为0的解
参数:
- f: 要求解的函数
- f_prime: 函数的导数
- x0: 初始猜测值
- tol: 容差（ ， ， ）
- max_iter: 最大迭代次数（ ， ）
返回:
- 解的近似值
"""
x = x0 # 初始猜测值
for _ in range ( max_iter ) :
fx = f ( x ) # 函数值
if abs ( fx ) < tol :
# 已达到容差要求，返回解的近似值
return x
fpx = f_prime ( x ) # 函数的导数值
if abs ( fpx ) < tol :
# 导数值过小，无法继续迭代
break
x - = fx / fpx # 牛顿迭代公式
# 迭代未收敛或超过最大迭代次数，
return None
def f ( x ) :
return x * * 2 - 4
def f_prime ( x ) :
return 2 * x
if __name__ == ' __main__ ' :
x0 = 1 # 初始猜测值
solution = newton_method ( f , f_prime , x0 )
print ( " 解的近似值: " , solution )
