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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}) $ ?

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

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