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n维散乱数据带自然边界条件多元多项式样条插值

徐应祥   

  1. 中山大学新华学院, 广州 510520
  • 收稿日期:2013-10-20 出版日期:2014-11-15 发布日期:2014-12-06
  • 基金资助:

    国家自然科学基金项目(11001060).

徐应祥. n维散乱数据带自然边界条件多元多项式样条插值[J]. 计算数学, 2014, 36(4): 407-426.

Xu Yingxiang. MULTIVARIATE POLYNOMIAL SPLINE INTERPOLATION WITH NATURAL BOUNDARY CONDITION FOR SCATTERED DATA OF nD[J]. Mathematica Numerica Sinica, 2014, 36(4): 407-426.

MULTIVARIATE POLYNOMIAL SPLINE INTERPOLATION WITH NATURAL BOUNDARY CONDITION FOR SCATTERED DATA OF nD

Xu Yingxiang   

  1. Xinhua College of Sun Yat-sen University, Guangzhou 510275, China
  • Received:2013-10-20 Online:2014-11-15 Published:2014-12-06
考虑n维散乱数据Hermit-Birkhoff型插值问题, 在使给定的目标泛极小的条件下,构造了一种带自然边界条件的多元多项式样条函数插值方法.重点研究了插值问题解的特征, 存在唯一性和构造方法, 并讨论了收敛性及误差, 最后给出了一些数值算例对方法进行验证.
Thinking the interpolation problem of Hermit-Birkhoff type for scattered data of n Dimension, under the condition of minimizing the given functional, a new multivariate polynomial spline interpolation with natural conditions have been constructed. The characterization, existence, uniqueness and construction of the solution of the interpolation problem are studied mainly. Convergence and error estimation are still discussed. Some numerical examples have been presented at last to illustrate the method.

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