中山大学学报自然科学版 ›› 2012, Vol. 51 ›› Issue (2): 22-29.

• 研究论文 • 上一篇    下一篇

散乱数据带自然边界条件三元多项式光顺样条

徐应祥1,2, 关履泰2, 许伟志2   

  1. (1.中山大学新华学院, 广东 广州 510520;2.中山大学科学计算与计算机应用系, 广东 广州 510275)
  • 收稿日期:2011-05-19 修回日期:1900-01-01 出版日期:2012-03-25 发布日期:2012-03-25
  • 通讯作者: 徐应祥

Tri-variable Polynomial Smoothing Spline with Natural Boundary Conditions for Scattered Data

XU Yingxiang1,2, GUAN Lutai2, XU Weizhi2

  

  1. (1. Xinhua College,Sun Yatsen University, Guangzhou 510520, China;2. Department of Scientific Computation and Computer Application, Sun Yat-sen University,Guangzhou 510275, China)
  • Received:2011-05-19 Revised:1900-01-01 Online:2012-03-25 Published:2012-03-25

摘要: 考虑对4维空间散乱数据的一种带自然边界条件的样条光顺。为使得给定的目标泛函达到极小,用Hilbert空间样条函数方法,得出其解可表为一个分片三元多项式,其表示形式简单,且系数可由线性代数方程组确定。最后给出一些数值例子进行了验证。

关键词: 散乱数据, 光顺, 自然边界条件, 样条

Abstract: A spline smoothing method with natural boundary conditions for scattered data of 4D are considered. In order to minimization the given objective functional, using the spline function methods of Hilbert space, the solution is constructed as a piecewise trivariable polynomial. Its expression is so simple and the coefficients are decided by a linear system. Some numerical examples are presented to illustrate the method.

Key words: scattered data, smoothing, natural boundary conditions, spline

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