Module for the Newton Interpolation Polynomial

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Background. Newton Interpolation Polynomial.   

Definition. Divided Differences.

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."

    .

Remark 2.  Mathematica's arrays are lists and the subscripts must start with  1  instead of  0.

Mathematica Subroutine (Newton Polynomial).

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  
  

Solution 1.

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

Solution 2.

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  .  

Solution 3.

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.  

Solution 4.

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

Research Experience for Undergraduates

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

Downloads (Newton Polynomial Newton Polynomial).  Download this Mathematica notebook.  

(c) John H. Mathews 2003