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Newton.py

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