Adaptive residual subsampling methods for radial basis function interpolation and collocation problems

被引：111
|
作者：
Driscoll, Tobin A. [1 ]
Heryudono, Alfa R. H. [1 ]
机构：
[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2007年 / 53卷 / 06期
关键词：
adaptive; radial basis functions; interpolation; collocation; residual subsampling;
D O I：
10.1016/j.camwa.2006.06.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct a new adaptive algorithm for radial basis functions (RBFs) method applied to interpolation, boundary-value, and initial-boundary-value problems with localized features. Nodes can be added and removed based on residuals evaluated at a finer point set. We also adapt the shape parameters of RBFs based on the node spacings to prevent the growth of the conditioning of the interpolation matrix. The performance of the method is shown in numerical examples in one and two space dimensions with nontrivial domains. (c) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：927 / 939
页数：13
相关论文
共 50 条
  • [41] RADIAL BASIS FUNCTION COLLOCATION FOR THE CHEMICAL MASTER EQUATION
    Zhang, Jingwei
    Watson, Layne T.
    Beattie, Christopher A.
    Cao, Yang
    [J]. INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2010, 7 (03) : 477 - 498
  • [42] An error analysis for radial basis function interpolation
    Michael J. Johnson
    [J]. Numerische Mathematik, 2004, 98 : 675 - 694
  • [43] Analysis of radial basis function interpolation approach
    Zou You-Long
    Hu Fa-Long
    Zhou Can-Can
    Li Chao-Liu
    Dunn Keh-Jim
    [J]. APPLIED GEOPHYSICS, 2013, 10 (04) : 397 - 410
  • [44] An error analysis for radial basis function interpolation
    Johnson, MJ
    [J]. NUMERISCHE MATHEMATIK, 2004, 98 (04) : 675 - 694
  • [45] Analysis of radial basis function interpolation approach
    You-Long Zou
    Fa-Long Hu
    Can-Can Zhou
    Chao-Liu Li
    Keh-Jim Dunn
    [J]. Applied Geophysics, 2013, 10 : 397 - 410
  • [46] Adaptive Radial Basis Function Partition of Unity Interpolation: A Bivariate Algorithm for Unstructured Data
    Cavoretto, Roberto
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2021, 87 (02)
  • [47] ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets
    Gao, Kaifeng
    Mei, Gang
    Cuomo, Salvatore
    Piccialli, Francesco
    Xu, Nengxiong
    [J]. SOFT COMPUTING, 2020, 24 (23) : 17693 - 17704
  • [48] Adaptive Radial Basis Function Partition of Unity Interpolation: A Bivariate Algorithm for Unstructured Data
    Roberto Cavoretto
    [J]. Journal of Scientific Computing, 2021, 87
  • [49] ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets
    Kaifeng Gao
    Gang Mei
    Salvatore Cuomo
    Francesco Piccialli
    Nengxiong Xu
    [J]. Soft Computing, 2020, 24 : 17693 - 17704
  • [50] Lagrange radial basis function collocation method for boundary value problems in 1D
    Al Arfaj, Kawther
    Levesly, Jeremy
    [J]. AIMS MATHEMATICS, 2023, 8 (11): : 27542 - 27572
12345