Menu Close

Newton Divided Difference Interpolation Method | Python

Newton divided difference interpolation is a method of constructing a polynomial that passes through a given set of points.

It is similar to Lagrange interpolation, but it tends to be more efficient for large sets of points.

Newton divided difference method in Python:

					import numpy as np

def newton_divided_difference(x, y, t):
    Find the Newton polynomial through the points (x, y) and return its value at t.
    #Newton Divided Difference Interpolation [By Bottom Science]
    # Check that the input arrays have the same length
    if len(x) != len(y):
        raise ValueError("The arrays x and y must have the same length.")

    # Initialize the polynomial
    p = [y[0]]

    # Loop over the differences
    for i in range(1, len(x)):
        # Initialize the term
        term = y[i]

        # Loop over the previous differences
        for j in range(i):
            term = (term - p[j]) / (x[i] - x[j])

        # Add the term to the polynomial

    # Evaluate the polynomial at t
    result = 0
    for i in range(len(x)):
        term = p[i]
        for j in range(i):
            term *= (t - x[j])
        result += term

    return result

x = [0, 1, 2]
y = [0, 1, 4]
t = 0.5
p = newton_divided_difference(x, y, t)

# Output - 0.25

More Related Stuff