Example 6.  Given  [Graphics:Images/NevilleAlgorithmMod_gr_495.gif]  and the nodes [Graphics:Images/NevilleAlgorithmMod_gr_496.gif] compute the entries in Aitken's tableau and Neville's tableau for evaluating  [Graphics:Images/NevilleAlgorithmMod_gr_497.gif]  at  [Graphics:Images/NevilleAlgorithmMod_gr_498.gif]  
Use the improved interpolation subroutines.

Solution 6.

Enter the function and nodes and point of evaluation.  

[Graphics:../Images/NevilleAlgorithmMod_gr_499.gif]

[Graphics:../Images/NevilleAlgorithmMod_gr_500.gif]

 

 

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

[Graphics:../Images/NevilleAlgorithmMod_gr_501.gif]

[Graphics:../Images/NevilleAlgorithmMod_gr_502.gif]

 

 

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

[Graphics:../Images/NevilleAlgorithmMod_gr_503.gif]

[Graphics:../Images/NevilleAlgorithmMod_gr_504.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005