Example 2.  Compare the "discrete interpolation polynomial" and "discrete least squares approximation" using equally spaced nodes.  
2 (a).  Use the function  [Graphics:Images/LegendrePolyMod_gr_46.gif]  on the interval  [Graphics:Images/LegendrePolyMod_gr_47.gif].  

Solution 2 (a).

[Graphics:../Images/LegendrePolyMod_gr_50.gif]



[Graphics:../Images/LegendrePolyMod_gr_51.gif]

[Graphics:../Images/LegendrePolyMod_gr_52.gif]

[Graphics:../Images/LegendrePolyMod_gr_53.gif]

[Graphics:../Images/LegendrePolyMod_gr_54.gif]

[Graphics:../Images/LegendrePolyMod_gr_55.gif]

[Graphics:../Images/LegendrePolyMod_gr_56.gif]

[Graphics:../Images/LegendrePolyMod_gr_57.gif]

[Graphics:../Images/LegendrePolyMod_gr_58.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005