# 径向基函数插值配置点的自适应选取算法An Adaptive Method for Choosing Collocation Points of RBF Interpolation

DOI: 10.12677/AAM.2016.51002, PDF, HTML, XML, 下载: 1,487  浏览: 3,245  国家自然科学基金支持

Abstract: 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.

 [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. http://dx.doi.org/10.1142/6437 [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. http://dx.doi.org/10.1016/S0377-0427(02)00352-7 [5] Iske, A. (2003) Progressive Scattered Data Filtering. Journal of Computational and Applied Mathematics, 158, 297- 316. http://dx.doi.org/10.1016/S0377-0427(03)00449-7 [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. http://dx.doi.org/10.1007/BF02432002 [8] Floater, M.S. and Iske, A. (1998) Thinning Algorithms for Scattered Data Interpolation. BIT Numerical Mathematics, 38, 705-720. http://dx.doi.org/10.1007/BF02510410 [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. http://dx.doi.org/10.1016/S0898-1221(01)00289-9 [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.