Report Number: CS-TR-80-799
Institution: Stanford University, Department of Computer Science
Title: Multidimensional additive spline approximation
Author: Friedman, Jerome H.
Author: Grosse, Eric
Author: Stuetzle, Werner
Date: May 1980
Abstract: We describe an adaptive procedure that approximates a function of many variables by a sum of (univariate) spline functions $s_m$ of selected linear combinations $a_m \cdot x$ of the coordinates $\theta (x) = \sum_{1\le m\le M} s_m (a_m \cdot x)$. The procedure is nonlinear in that not only the spline coefficients but also the linear combinations are optimized for the particular problem. The sample need not lie on a regular grid, and the approximation is affine invariant, smooth, and lends itself to graphical interpretation. Function values, derivatives, and integrals are cheap to evaluate.
http://i.stanford.edu/pub/cstr/reports/cs/tr/80/799/CS-TR-80-799.pdf