Example 7.  Given  [Graphics:Images/NevilleAlgorithmMod_gr_515.gif]  and the nodes [Graphics:Images/NevilleAlgorithmMod_gr_516.gif] compute the entries in Aitken's tableau and Neville's tableau for evaluating  [Graphics:Images/NevilleAlgorithmMod_gr_517.gif]  at  [Graphics:Images/NevilleAlgorithmMod_gr_518.gif]  
Use the improved interpolation subroutines with matrices.

Solution 7.

Enter the function and nodes and point of evaluation.  

[Graphics:../Images/NevilleAlgorithmMod_gr_519.gif]

[Graphics:../Images/NevilleAlgorithmMod_gr_520.gif]

 

 

7 (a).  Compute the values for Neville's tableau.

[Graphics:../Images/NevilleAlgorithmMod_gr_521.gif]

[Graphics:../Images/NevilleAlgorithmMod_gr_522.gif]

 

 

7 (b).  Compute the values for Aitken's tableau.

[Graphics:../Images/NevilleAlgorithmMod_gr_523.gif]

[Graphics:../Images/NevilleAlgorithmMod_gr_524.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005