Natural interpolating splines of arbitrary degree (Q1386609)

For the interpolation of the values \(y_0,\dots,y_N\) at the nodes \(x_0,\dots,x_N\), the authors propose the construction of splines \(S(x)=y_0 + \sum_{k=0}^m a_k (x-x_0)^k+\sum_{n=1}^{N-1} b_n(x-x_n)_+^m\), \(S(x_n)=y_n\), \(n=1,\dots,N\), such that \(\sum_{n=1}^{N-1} r_n b_n^2\to \min\), \(r_n=\rho_n/(x_{n+1}-x_{n-1})\), where \(\rho_n\) are given real nonnegative constants. Some pointwise error estimates and numerical examples are given.