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 (a).  Use the function  [Graphics:Images/LegendrePolyMod_gr_26.gif].  

Solution 1 (a).

[Graphics:../Images/LegendrePolyMod_gr_28.gif]



[Graphics:../Images/LegendrePolyMod_gr_29.gif]

[Graphics:../Images/LegendrePolyMod_gr_30.gif]

[Graphics:../Images/LegendrePolyMod_gr_31.gif]

[Graphics:../Images/LegendrePolyMod_gr_32.gif]

[Graphics:../Images/LegendrePolyMod_gr_33.gif]

[Graphics:../Images/LegendrePolyMod_gr_34.gif]

[Graphics:../Images/LegendrePolyMod_gr_35.gif]

[Graphics:../Images/LegendrePolyMod_gr_36.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005