Example 1. Construct the natural cubic spline for the points that has the endpoint constraints .
Solution 1.
(c) John H. Mathews 2003
![[Graphics:Images/CubicSplinesMod_gr_25.gif]](../Images/CubicSplinesMod_gr_25.gif){kind=small}
that
has the endpoint constraints ![[Graphics:Images/CubicSplinesMod_gr_26.gif]](../Images/CubicSplinesMod_gr_26.gif){kind=small}
. that
has the endpoint constraints . ![[Graphics:../Images/CubicSplinesMod_gr_27.gif]](../Images/CubicSplinesMod_gr_27.gif)
![[Graphics:../Images/CubicSplinesMod_gr_28.gif]](../Images/CubicSplinesMod_gr_28.gif)
![[Graphics:../Images/CubicSplinesMod_gr_29.gif]](../Images/CubicSplinesMod_gr_29.gif){kind=small}
![[Graphics:../Images/CubicSplinesMod_gr_30.gif]](../Images/CubicSplinesMod_gr_30.gif){kind=small}
![[Graphics:../Images/CubicSplinesMod_gr_31.gif]](../Images/CubicSplinesMod_gr_31.gif){kind=small}
![[Graphics:../Images/CubicSplinesMod_gr_32.gif]](../Images/CubicSplinesMod_gr_32.gif){kind=small}
![[Graphics:../Images/CubicSplinesMod_gr_33.gif]](../Images/CubicSplinesMod_gr_33.gif)