Example 1.  Compare the "discrete interpolation polynomial" and "discrete least squares approximation" using equally spaced nodes on the interval  [Graphics:Images/LegendrePolyMod_gr_25.gif].  
1 (b).  Use the function  [Graphics:Images/LegendrePolyMod_gr_27.gif].  

Solution 1 (b).

[Graphics:../Images/LegendrePolyMod_gr_37.gif]



[Graphics:../Images/LegendrePolyMod_gr_38.gif]

[Graphics:../Images/LegendrePolyMod_gr_39.gif]

[Graphics:../Images/LegendrePolyMod_gr_40.gif]

[Graphics:../Images/LegendrePolyMod_gr_41.gif]

[Graphics:../Images/LegendrePolyMod_gr_42.gif]

[Graphics:../Images/LegendrePolyMod_gr_43.gif]

[Graphics:../Images/LegendrePolyMod_gr_44.gif]

[Graphics:../Images/LegendrePolyMod_gr_45.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005