Mathematical Sciences: Theory and Applications of Spline Functions

数学科学：样条函数的理论与应用

• 批准号: 9208413
• 负责人: Larry Schumaker
• 金额: $ 14.7万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1996-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208413&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Applications; Spline

The aim of this research is to contribute both the theory and applications of multivariate splines. The theoretical questions to be addressed involve dimensions of multivariate spline spaces, construction of local bases for these spaces, and study of their approximation power. In addition to the traditional spaces defined on triangulations, new spaces defined on triangulations of the sphere or other 3D objects will also be investigated. The applications involve the use of simulated annealing to construct optimal triangulations, the design of shape preserving interpolation and data fitting methods, the use of radial basis functions for penalized least squares fitting, and adaptive methods for fitting functions of many variables.

本研究的目的是为多元样条的理论和应用做出贡献。 要解决的理论问题包括多元样条空间的维数、这些空间的局部基的构造以及它们的逼近能力的研究。 除了在三角剖分上定义的传统空间之外，还将研究在球体或其他 3D 对象的三角剖分上定义的新空间。 这些应用包括使用模拟退火来构造最佳三角剖分、保形插值和数据拟合方法的设计、使用径向基函数进行惩罚最小二乘拟合以及用于拟合多变量函数的自适应方法。