Example 2.  Compare the "discrete interpolation polynomial" and "discrete least squares approximation" using equally spaced nodes.  
2 (b).  Use the function  [Graphics:Images/LegendrePolyMod_gr_48.gif]  on the interval  [Graphics:Images/LegendrePolyMod_gr_49.gif]

Solution 2 (b).

[Graphics:../Images/LegendrePolyMod_gr_59.gif]



[Graphics:../Images/LegendrePolyMod_gr_60.gif]

[Graphics:../Images/LegendrePolyMod_gr_61.gif]

[Graphics:../Images/LegendrePolyMod_gr_62.gif]

[Graphics:../Images/LegendrePolyMod_gr_63.gif]

[Graphics:../Images/LegendrePolyMod_gr_64.gif]

[Graphics:../Images/LegendrePolyMod_gr_65.gif]

[Graphics:../Images/LegendrePolyMod_gr_66.gif]

[Graphics:../Images/LegendrePolyMod_gr_67.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005