Mathematical Sciences: Spline Functions and Applications

8902331舒梅克，这项研究的目的是为多元样条的理论和应用做出贡献。要解决的理论问题涉及维度、最小支撑基函数的构造以及逼近能力与次数和光滑性的相互作用。这些应用包括对散乱数据进行曲面拟合，以及在计算机辅助设计中使用多变量样条线。特别讨论了最小能量插值法、基于径向函数和多元样条基的惩罚最小二乘法以及保形曲面拟合法的构造。

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.