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import numpy as np
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# 给定数据
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t_values = np.array([0, 10, 15, 20, 22.5, 30])
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v_values = np.array([0, 227.04, 362.78, 517.35, 602.97, 901.67])
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# 计算Newton插值法所需的差商
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def divided_diff(t_values, v_values):
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# 用给定的数值初始化差商数组
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differences = v_values.copy()
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# 遍历每个数据点，计算差商
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for i in range(1, len(t_values)):
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for j in range(len(t_values) - 1, i - 1, -1):
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differences[j] = (differences[j] - differences[j - 1]) / (t_values[j] - t_values[j - i])
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return differences
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# 使用Newton插值法寻找 t=16 时的速度
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def newton_interpolation(t_values, v_values, target_t):
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differences = divided_diff(t_values, v_values)
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p = differences[0]
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for i in range(1, len(t_values)):
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term = differences[i]
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for j in range(i):
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term *= (target_t - t_values[j])
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p += term
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return p
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t_target = 16
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velocity_at_16 = newton_interpolation(t_values, v_values, t_target)
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print(f"使用Newton插值法，t=16 秒时的速度为: {velocity_at_16:.2f} m/s")
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