# End conditions on cubic splines interpolation

I'm currently working on cubic splines interpolation. My question has to do with the end conditions. Instead of using natural or clamped cubic splines, I am asked to use the following condition :

$S_{1} = S_{2}$ and $S_{n} = S_{n-1}$

but I am not pretty sure how this is applied.

Could anyone help me clear this out?

EDIT

I am editting due to the first comment. On which points do I appply this condition? $S_{1}(x_{2}) = S_{2}(x_{2})$ is a condition that I've already used and $S_{1}(x_{1}) = S_{2}(x_{2})$ leads to a contradiction...So is it something like $S_{1}(x_{1}) = S_{2}(x_{1})$ ?

• In addition to the continuity conditions at knots (nodes), you use these two additional linear equations to determine the cubic spline coefficients. – hardmath Dec 22 '15 at 2:59