Module for the Newton Interpolation Polynomial

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Background. Newton Interpolation Polynomial.

Animations (Newton InterpolationPolynomial  Newton InterpolationPolynomial).  Internet hyperlinks to animations.

Algorithm (Newton Interpolation Polynomial).   To construct and evaluate the Newton polynomial of  degree    that passes through the n+1 points  ,  for

where

and

Remark 1.  Newton polynomials are created "recursively."

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Mathematica Subroutine (Newton Polynomial).

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Example 1.   Form several 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

Example 2.  Error Analysis.  Investigate the error for the Newton polynomial approximations in Example 1.

Example 3.  What is the maximum over the interval    for each of the quantities
3 (a).  Find  .
3 (b).  Find  .
3 (c).  Find  .
3 (d).  Find  .
3 (e).  Find  .

Example 4.  Application to number theory.
4 (a).  Find the formula for the sum of the first  n  integers.
4 (b).  Find the formula for the sum of the squares of the first  n integers.

Old Lab Project (Newton Interpolation Polynomial  Newton Interpolation Polynomial).  Internet hyperlinks to an old lab project.

Newton Interpolation Polynomial  Newton Interpolation Polynomial  Internet hyperlinks to web sites and a bibliography of articles.

(c) John H. Mathews 2003