8902331 Schumaker The aim of this research is to contribute to both the theory and applications of multivariate splines. The theoretical questions to be addressed relate to dimension, the construction of minimally supported basis functions, and the interplay of approximation power with degree and smoothness. The applications involve fitting surfaces to scattered data and the use of multivariate splines in computer-aided design. In particular, minimal energy interpolants, penalized least squares methods based on radial functions and multivariate splines, and construction of shape-preserving surface fitting methods are considered.
