ABSTRACT
The setting of graduation enjoyed relative simplicity due to the sequential, equidistant character of observations. While differences are still possible, a revolutionary leap forward was accomplished by Schoenberg, who recognized that the Whittaker graduation can be formulated in a very general functional setting, and pointed out its connection to splines, the effective interpolation vehicle in numerical analysis. All multivariate proposals pretty much had to forgo the hopes for a representer theorem. In such situations, the alternative was to act as if such characterizations existed: to restrict the fits to finite-dimensional domains that were deemed reasonable, and study penalized fitting on those domains. Unlike the development of unpenalized regression fitting the initial work in the penalized domain did not see that much variety and rather adhered to the ideal of "wonderful simplicity" in the sense of Gauss: all formulations were quadratic.
