I have some trouble with this problem:
Consider that you have the following data $(x_i ,y_i)$ for $I=1...m$, where $0 \leq x_i \leq L$ How could you build a cubic spline defined in the following segments $\left [ s_{j} , s_{j+1} \right ]$ for $j= 0 \ ... \ J$ (and $m\geq J$) using Lagrange Multipliers in order to minimize the error?
Thanks for any directions