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 \[ \phi (x) = \sum_{1 \leqq m \leqq M} {s_m ( a_m \cdot x)}. \] 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 inexpensive to evaluate.

Keywords

MathematicsSpline (mechanical)UnivariateAffine transformationNonlinear systemApplied mathematicsGridB-splineCombinatoricsMathematical analysisPure mathematicsGeometryMultivariate statisticsStatistics

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Publication Info

Year
1983
Type
article
Volume
4
Issue
2
Pages
291-301
Citations
90
Access
Closed

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Cite This

Jerome H. Friedman, Eric H. Grosse, Werner Stuetzle (1983). Multidimensional Additive Spline Approximation. SIAM Journal on Scientific and Statistical Computing , 4 (2) , 291-301. https://doi.org/10.1137/0904023

Identifiers

DOI
10.1137/0904023

Data Quality

Data completeness: 81%