Exercise 1.13.7. In Sect. 1.7 we set up the interpolating cubic spline problem as one of fitting a saturated linear model that is forced be continuous, have continuous first and second derivatives, and have 0 as the second derivative on the boundaries.

In our discussion, the dots are only connected implicitly because a saturated model must fit every data point perfectly. Show that you can find the parameters of the fitted polynomials without using least squares by setting up a system of linear equations requiring the polynomials to connect the (xi, yi) dots along with satisfying the derivative conditions.