Example 1.   Form the Newton polynomials of degree  n = 1,2, 3, 4, and 5  for the function    over the interval    using equally spaced nodes selected from the following list  
  
Solution 1 (b).

Use the nodes    to construct the Newton interpolation polynomial  ,  of degree n = 2, and compare it to the polynomial constructed with Mathematica's InterpolatingPolynomial procedure.

The polynomial obtained with Mathematica's InterpolatingPolynomial procedure is the nested form of the Newton polynomial.

Notice that    is obtained from    by adding one more term.

Now graph the function and polynomial, and interpolation nodes.

(c) John H. Mathews 2004