计算数学
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计算数学  2011, Vol. 33 Issue (1): 37-47    DOI:
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三奇次散乱点多项式自然样条插值
徐应祥, 关履泰, 许伟志
中山大学科学计算与计算机应用系, 广州 510275
TRIVARIATE ODD DEGREE POLYNOMIAL NATURAL SPLINE INTERPOLATION FOR SCATTERED DATA
Xu Yingxiang, Guan Lvtai, Xu Weizhi
Department of Scientific Computation and Computer Application, Sun Yat-sen University, Guangzhou 510275, China
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摘要 

为解决较为复杂的三变量散乱数据插值问题,提出了一种三元多项式自然样条插值方法.在使得对一种带自然边界条件的目标泛函极小的情况下,用Hilbert空间样条函数方法,构造出了插值问题的解,并可表为一个分块三元三奇次多项式.其表示形式简单,且系数可由系数矩阵对称的线性代数方程组确定.

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关键词散乱数据插值   三奇次多项式   自然样条     
Abstract

To solve the complicated interpolation problem for trivariate scattered data, a trivariate polynomial natural spline interpolation method is proposed. In the case of minimizing the objective functional with natural boundary conditions, the solution of the interpolation problem is constructed by the spline function methods of Hilbert space and in every block is a trivariate odd degree polynomial. Its expression is so simple and the coefficients can be decided by a linear system whose coefficient matrix is symmetry.

Key wordsscattered data interpolation   trivariate odd degree polynomial   natural spline   
收稿日期: 2009-04-03;
基金资助:

教育部高等学校博士点科研基金(200805581022)和广东省自然科学基金(7003624)资助项目.

引用本文:   
. 三奇次散乱点多项式自然样条插值[J]. 计算数学, 2011, 33(1): 37-47.
. TRIVARIATE ODD DEGREE POLYNOMIAL NATURAL SPLINE INTERPOLATION FOR SCATTERED DATA[J]. Mathematica Numerica Sinica, 2011, 33(1): 37-47.
 
[1] Tony F Chen, Jianhong Shen. 图像处理与分析:变分, PDE, 小波及随机方法(影印版)[M]. 北京: 科学出版社, 2009.
[2] 唐泽圣.三维数据场可视化[M].北京:清华大学出版社, 1999.
[3] 钱归平,童若锋,彭文,董金祥.保持特征区域的点云自适应网格重建[J].中国图象图形学报, 2009, 14(1):1 48-154.
[4] Kazhdan M, Bolitho M, Hoppe H. Posson surface reconstruction[J]. in: Proceeding of Eurogrouphics Synposium on Geometry Processing. Cagliari, Italy, 2006: 61-70.
[5] 王仁宏.多元样条及其应用[M]. 北京: 科学出版社, 1992.
[6] Guan L T, Bin Liu. Surface design by natural Splines over refined grid points[J]. Jouneral of Computational and Applied Mathematics, 2004, 163(1): 107-115.
[7] 关履泰,覃廉,张健.用参数样条插值挖补方法进行大规模散乱数据曲面造型[J].计算机辅助设计与图形学学报, 2006, 18(3): 372-377.
[8] Lai M J, Schumaker L L. Spline functions over triangulations[M]. London: Cambridge University Press, 2007.
[9] Lai M J. Multivarariate Splines for data fitting and approximation, Approximation Theory XII, San Antonio[M]. 2007, edited by M.Neamtu and L.L.Schumaker, Nashboro Press,Brentwood, 2008: 210-228.
[10] Zhou T H, Han D F, Lai M J. Energy minimization method for scattered data Hermit interpolation [J]. Applied Numerical Mathematics, 2008, 58: 646-659.
[11] 吴宗敏.散乱数据拟合的模型、方法和理论[M]. 北京: 科学出版社, 2007.
[12] Li Y S, Guan L T. Bivariate polynomial natural Splines interpolation to seattered data[J]. Jonural of Computational Mathematics, 1990, 8(2): 135-146.
[13] Chui C K, Guan L T. Multivariate polynomial natural spline for interpolation of scattered data and other applications[J]. in:Workship on Comurtational Geometry, eds.A. Conte et al. World Sciedtific 1993, 77-98.
[14] Guan L T. Bivariate polynomial natural Spline interpolation algorithms with local basis for scattered data[J]. J. Comp. Anal. and Appl., 2003, 2(1): 77 -101.
[15] 关履泰,许伟志,朱庆勇.一种双三次散乱数据多项式自然样条插值[J].中山大学学报(自然科学版), 2008, 47(5): 1-4.
[16] Laurent P J. Approximation et optimization[M]. Hermann, Paris, 1972.
[1] 许伟志, 关履泰, 韩乐. 散乱数据(2m-1,2n-1)次多项式自然样条插值[J]. 计算数学, 2009, 30(4): 255-265.

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