= Natural cubic cardinal spline endpoint rows
{title2=$c_{-1}-2c_0+c_1=c_{m-1}-2c_m+c_{m+1}=0$}
For the centered <Cardinal cubic B-spline> $\beta$ with knot values $1/6,4/6,1/6$, write $s(x)=\sum_{j=-1}^{m+1}c_j\beta(x/h-j)$ on $[0,mh]$. <interpolation> gives $c_{i-1}+4c_i+c_{i+1}=6u(ih)$ for $i=0,\ldots,m$. Since $\beta''(0)=-2$ and $\beta''(\pm1)=1$, the natural endpoint conditions $s''(0)=s''(mh)=0$ give the displayed extra two rows. These supply the two equations missing from <interpolation> alone.
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