计算数学
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计算数学  2011, Vol. 33 Issue (4): 423-446    DOI:
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散乱数据带自然边界条件三元多项式样条插值
徐应祥1,2, 喻高航3, 关履泰1
1. 中山大学新华学院, 广州 510520;
2. 西北师范大学数学与信息科学学院, 兰州 730070;
3. 赣南师范学院数学与计算机科学学院, 江西赣州 341000
TRIVARIATE POLYNOMIAL SPLINE INTERPOLATION WITH NATURAL BOUNDARY CONDITION FOR SCATTERED DATA
Xu Yingxiang1,2, Yu Gaohang3, Guan Lutai1
1. Department of Scientific Computation and Computer Application, Sun Yat-sen University, Guangzhou 510275, China;
2. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China;
3. College of Mathematics and Computer Science, Gannan normal University, Ganzhou 341000, Jiangxi, China
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摘要 为解决4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三元多项式样条函数方法. 研究了插值问题解的特征, 存在唯一性, 收敛性及误差, 最后给出了一些数值算例.
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关键词散乱数据   自然边界条件   三元多项式   自然样条     
Abstract: To solve the interpolation problem of Hermit-Birkhoff type for scattered data of 4D, under the condition of minimizing the given functional, a new trivatiate polynomial spline interpolation with natural conditions have been constructed. The characterization, existence, uniqueness, convergence and error estimation of the solution of the interpolation problem have been studied carefully. Some numerical examples have been presented at last to illustrate the method.
Key wordsscattered data   interpolation   tri-cubic polynomial   natural spline   
收稿日期: 2011-08-30;
基金资助:

国家自然科学基金项目(11001060).

引用本文:   
. 散乱数据带自然边界条件三元多项式样条插值[J]. 计算数学, 2011, 33(4): 423-446.
. TRIVARIATE POLYNOMIAL SPLINE INTERPOLATION WITH NATURAL BOUNDARY CONDITION FOR SCATTERED DATA[J]. Mathematica Numerica Sinica, 2011, 33(4): 423-446.
 
[1] Chen T F, Shen J. 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] de Boor C. Bicubic spline interpolation[J]. J. Math. and Phys. 1962, 41: 212-218.
[4] Schumaker L L. Fitting surfaces to scattered data, 203-268, in Approximation Theory II[M]. Lorentz G G, Chui CK, Schumaker L L. eds., New York: Academic Press, 1976.
[5] Frank R. Scattered data interpolation: tests of some methods[J]. Math. of Comput., 1982, 38: 181-200.
[6] Micchelli C A. Interpolation of scatteted data: distance matrices and conditionally positive definite functions[J]. Constr.Approx., 1986, 2: 11-22.
[7] 王仁宏.多元样条及其应用[M].北京:科学出版社, 1992.
[8] Lai M J. Multivarariate Splines for data fitting and approximation, 210-228, in Approximation Theory XII[M], San Antonio, 2007, Neamtu M., Schumaker L.L., eds., Brentwood: Nashboro Press, 2008.
[9] 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.
[10] Amidror I. Scattered data interpolation methods for electronic imaging systems: a survey[J]. Journal of Electronic Imaging. 2002, 11(2): 157-176.
[11] Chui C K, Shumaker S S,Wang R H. On spaces of piecewise polynomial with boundary cnditions, II type-1 triangulations, 51-66, in Second Edmonton Conference on Approximation Theory[M], Ditzian Z, Meir A, Riemenschneider S and Shrma A eds., Provindence: American Mathematical Society, 1983.
[12] Chui C K, Wang R H. Multivariate spline spaces[J]. J.Math.Anal.Appl, 1983, 94: 197-221.
[13] Lai M J, Schumaker L L.Spline Functions Over Triangulations[M]. London: Cambridge University Press, 2007.
[14] de Boor C, Höllig K, Riemenschneider S. Box Splines[M], Berlin: Springer-Verlag, 1993.
[15] Chui C K, Lai M J. On multivariate vertex splines and applications, 19-36, in Topics in Multivariate Approximation[M], Chui C K, Schumaker L L, Utreras F eds. New York: Academic Press, 1987.
[16] Chui C K, Lai M J. Multivariate vertex splines and finite elements[J]. J. Approx. Theory, 1990, 60: 245-343.
[17] Chui C K, He T X. On bivariate C1 quadratic finite elements and vertes splines[J]. Math. Comp., 1990, 54: 169-187.
[18] Li Y S. Multivariate optimal interpolation to scattered data throughout a rectangle I-with continuous boundary conditions[J], CAT 55, Texax A&M University, 1984.
[19] Li Y S, Guan L T. Bivariate polynomial natural Splines interpolation to seattered data[J]. Jonural of Computational Mathematics, 1990, 8(2): 135-146.
[20] 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.
[21] 关履泰. 散乱数据的多项式自然样条光顺与广义插值[J]. 计算数学, 1993, 17(4): 383-401.
[22] Guan L T, Liu B. Surface design by natural Splines over refined grid points[J]. J. Comp. Appl. Math, 2004, 163(1): 107-115.
[23] 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.
[24] 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]. 数值计算与计算机应用, 2009, 30(4): 255-265. 浏览
[25] 徐应祥, 关履泰, 许伟志. 三奇次散乱点自然样条插值[J]. 计算数学, 2011, 33(1): 37-47. 浏览
[26] Adams R A. Sobolev Spaces[M]. New York: Academic Press, 1975.
[27] Evans L C. Partial Differential Equations[M]. Providence: American Mathematical Society, 1998.
[28] Goldberg S. Unbounded Linear Operator: Theory and Application[M]. New York: McGraw-Hill, Inc. 1966.
[29] Bezhaev A Y, Vasilenko V A. Variational Theory of Splines[M]. New York: Kluwer Academic/Plenum Publishers, 2001.
[30] Kouibia A, Pasadas M. Approximation by interpolating variational splines[J]. J. Comp. Appl. Math., 2008, 218: 342-349.
[1] 徐应祥, 关履泰, 许伟志. 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.
[2] 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.
[3] 关履泰. 用广义交互确认方法选择良好参数进行多元多项式散乱数据自然样条光顺[J]. 计算数学, 1998, 20(4): 383-392.

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