Example 1.  Construct the natural cubic spline for the points [Graphics:Images/CubicSplinesMod_gr_25.gif]  that has the endpoint constraints   [Graphics:Images/CubicSplinesMod_gr_26.gif].  

Solution 1.

[Graphics:../Images/CubicSplinesMod_gr_27.gif]


[Graphics:../Images/CubicSplinesMod_gr_28.gif]

[Graphics:../Images/CubicSplinesMod_gr_29.gif]
[Graphics:../Images/CubicSplinesMod_gr_30.gif]

If more information is needed, we can look at the coefficients that form the cubic spline.

[Graphics:../Images/CubicSplinesMod_gr_31.gif]


[Graphics:../Images/CubicSplinesMod_gr_32.gif]
[Graphics:../Images/CubicSplinesMod_gr_33.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004