AAM  >> Vol. 5 No. 1 (February 2016)

    An Adaptive Method for Choosing Collocation Points of RBF Interpolation

  • 全文下载: PDF(437KB) HTML   XML   PP.8-14   DOI: 10.12677/AAM.2016.51002  
  • 下载量: 1,225  浏览量: 2,871   国家自然科学基金支持


刘雨,姜自武:临沂大学理学院,山东 临沂;
刘广磊:临沂大学信息学院,山东 临沂;
龚佃选:河北联合大学理学院,河北 唐山

自适应算法配置点径向基函数贪婪算法Adaptive Method Collocation Points Radial Basis Function Greedy Algorithm



Radial basis function (RBF) is one of effective meshfree methods for interpolation on high dimen-sional scattered data. Since the approximation quality and stability seriously depend on the dis-tribution of the collocation points, it is urgent to find algorithm of choosing optimal point sets for the reconstruction process. In this paper, we give a short overview of existing algorithms including thinning algorithm, greedy algorithm, and so on. A new adaptive data-dependent method is pro-vided at the end with a numerical example to show its efficiency.

刘雨, 刘广磊, 姜自武, 龚佃选. 径向基函数插值配置点的自适应选取算法[J]. 应用数学进展, 2016, 5(1): 8-14. http://dx.doi.org/10.12677/AAM.2016.51002


[1] 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.
[2] Fasshauer, G.E. (2007) Meshfree Approximation Methods with Matlab. World Scientific, Singapore.
[3] Franke, R. (1982) Scattered Data Interpolation, Test of Some Methods. Ma-thematics of Computation, 38, 181-200.
[4] Dyn, N., Floater, M.S. and Iske, A. (2002) Adaptive Thinning for Biva-riate Scattered Data. Journal of Computational and Applied Mathematics, 145, 505-517.
[5] Iske, A. (2003) Progressive Scattered Data Filtering. Journal of Computational and Applied Mathematics, 158, 297- 316.
[6] Wendland, H. (2005) Scattered Data Approximation (Cambridge Monographs on Applied and Computational Mathematics; 17). Cambridge University Press, Cam-bridge.
[7] Schaback, R. (1995) Error Estimates and Condition Numbers for Radial Basis Function Interpolation. Advances in Computational Mathematics, 3, 251-264.
[8] Floater, M.S. and Iske, A. (1998) Thinning Algorithms for Scattered Data Interpolation. BIT Numerical Mathematics, 38, 705-720.
[9] Behrens, J. and Iske, A. (2002) Grid-Free Adaptive Semi-Lagrangian Advection Using Radial Basis Functions. Computers and Mathematics with Applications, 43, 319-327.
[10] Marchi, S.D. (2003) On Optimal Center Locations for Radial Basisfunction Interpolation: Computational Aspects. Rendiconti del Seminario Matematico Università e Poli-tecnico di Torino (Splines Radial Basis Functions and Applications), 61, 343-358.
[11] Xu, B.Z., Zhang, B.L. and Wei, G. (1994) Neural Network Theory and Its Application. South China University of Technology Press, Guangzhou.