We describe an adaptive procedure that approximates a function of many variables by a sum of (univariate) spline functions sₘ of selected linear combinations aₘ · x of the coordinates \[ φ (x) = ∑1 m M {s_m ( a_m · x)}. \] 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 inexpensive to evaluate.
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Friedman et al. (1983) studied this question.
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