Mathematical Sciences: Spline Functions and Applications

8902331 舒梅克 这项研究的目的是促进双方的 多元样条的理论与应用 的 要解决的理论问题涉及到尺寸， 最小支撑基函数的构造， 逼近能力与度和光滑性的相互作用。 这些应用程序涉及将曲面拟合到分散的数据， 在计算机辅助设计中使用多元样条。 在 特别的，最小能量插值，惩罚最小 基于径向函数和多元的平方方法 样条曲线和保形曲面拟合的构造 方法被考虑。

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.