It is not too difficult to construct a convolutional basis with more
accurate interpolation properties than those of B-splines, for example
by sacrificing the function smoothness. The following piece-wise cubic
function has a lower smoothness than in
equation (46) but slightly better interpolation behavior:
Blu et al. (1998) have developed a general approach for constructing non-smooth piece-wise functions with optimal interpolation properties. However, the gain in accuracy is often negligible in practice. In the rest of the dissertation, I use the classic and better tested B-spline method.