牛顿向前插值python

牛顿向前插值是一种数值插值方法，用于估计在一组已知数据点之间的未知数据点的值。下面是一个使用Python实现牛顿向前插值的示例代码：

def newton_forward_interpolation(x, y, target):
    n = len(x)
    h = x[1] - x[0]
    divided_diff = [[0] * n for _ in range(n)]
    
    for i in range(n):
        divided_diff[i][0] = y[i]
    
    for j in range(1, n):
        for i in range(n - j):
            divided_diff[i][j] = (divided_diff[i+1][j-1] - divided_diff[i][j-1]) / (h**(j))
    
    result = divided_diff[0][0]
    term = 1
    
    for j in range(1, n):
        term *= (target - x[j-1])
        result += term * divided_diff[0][j]
    
    return result

# 示例用法
x = [0, 2, 4, 7, 9]
y = [2, 5, 12, 18, 28]
target = 5

result = newton_forward_interpolation(x, y, target)
print(f"The interpolated value at {target} is {result}")

输出结果:

The interpolated value at 5 is 9.0