牛顿插值法python代码

以下是使用Python实现的牛顿插值法的代码：

def newton_interpolation(x, y, x_new):
    """
    Newton interpolation implementation.
    :param x: list, x values
    :param y: list, y values
    :param x_new: float, new x value to interpolate
    :return: float, interpolated y value
    """
    n = len(x)
    coefficients = []
    
    # calculate divided differences
    for i in range(n):
        coefficients.append(y[i])
        for j in range(i-1, -1, -1):
            coefficients[j] = (coefficients[j+1] - coefficients[j]) / (x[i] - x[j])
    
    # calculate interpolated value
    result = coefficients[-1]
    for i in range(n-2, -1, -1):
        result = coefficients[i] + (x_new - x[i]) * result
    
    return result

其中，`x`和`y`是已知数据点的x值和y值，`x_new`是要插值的新x值。函数返回插值得到的y值。