Example 1.   Form the Newton polynomials of degree  n = 1,2, 3, 4, and 5  for the function  [Graphics:Images/NewtonPolyMod_gr_109.gif]  over the interval  [Graphics:Images/NewtonPolyMod_gr_110.gif]  using equally spaced nodes selected from the following list  
[Graphics:Images/NewtonPolyMod_gr_111.gif]  
Solution 1 (f).

[Graphics:../Images/NewtonPolyMod_gr_212.gif]

[Graphics:../Images/NewtonPolyMod_gr_213.gif]

[Graphics:../Images/NewtonPolyMod_gr_214.gif]

[Graphics:../Images/NewtonPolyMod_gr_215.gif]

[Graphics:../Images/NewtonPolyMod_gr_216.gif]

[Graphics:../Images/NewtonPolyMod_gr_217.gif]

[Graphics:../Images/NewtonPolyMod_gr_218.gif]

[Graphics:../Images/NewtonPolyMod_gr_219.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004