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