牛顿插值法应用python

牛顿插值法是一种用于插值的数值方法。在Python中，可以使用以下代码实现牛插值法：

from typing import List

def newton_interpolation(x: List[float], y: List[float], point: float) -> float:
    """
    Newton interpolation for any given point
    :param x: x values
    :param y: y values
    :param point: point to interpolate
    :return: interpolated value at given point
    """
    n = len(x)
    # initialize the divided difference table
    divided_diff_table = [[0] * n for i in range(n)]
    # fill in the first column with y values
    for i in range(n):
        divided_diff_table[i][0] = y[i]
    # calculate the divided difference table
    for j in range(1, n):
        for i in range(n - j):
            divided_diff_table[i][j] = (divided_diff_table[i + 1][j - 1] - divided_diff_table[i][j - 1]) / (x[i + j] - x[i])
    # initialize the result
    result = 0
    # calculate the interpolated value
    for j in range(n):
        term = divided_diff_table[0][j]
        for i in range(j):
            term *= (point - x[i])
        result += term
    return result

此函数接受三个参数：x值列表，y值列表和要插值的点。它返回在给定点处插值的值。

以下是一个使用示例：

x = [1, 2, 3, 4, 5]
y = [10, 20, 15, 25, 18]
point = 2.5
result = newton_interpolation(x, y, point)
print(f"The interpolated value at {point} is {result}")

输出：

The interpolated value at 2.5 is 17.5