牛顿插值法，数值分析第二章习题2

import numpy as np

def newton_interpolation_with_table(x, y, xi):
    """
    x : array_like, shape (n,)
        data points x-coordinates
    y : array_like, shape (n,)
        data points y-coordinates
    xi : scalar
        the x value where interpolation is computed
    """
    n = len(x)
    # Divided difference table
    divided_diff = np.zeros((n, n))
    divided_diff[:, 0] = y

    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]) / (x[i + j] - x[i])

    # Print divided difference table
    print("Divided Difference Table:")
    print(divided_diff)

    # Interpolating polynomial
    result = divided_diff[0, 0]
    product_terms = 1.0
    for i in range(1, n):
        product_terms *= (xi - x[i - 1])
        result += divided_diff[0, i] * product_terms

    return result

# Exa