Sobolev Error Estimates and a Bernstein Inequality for Scattered Data Interpolation via Radial Basis Functions

2006 ◽  
Vol 24 (2) ◽  
pp. 175-186 ◽  
Author(s):  
Francis J. Narcowich ◽  
Joseph D. Ward ◽  
Holger Wendland
Keyword(s):  
Error Estimates ◽  
Radial Basis Functions ◽  
Bernstein Inequality ◽  
Scattered Data ◽  
Basis Functions ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Radial Basis

scholarly journals Scattered Data Interpolation and Approximation with Truncated Exponential Radial Basis Function

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1101 ◽  
Author(s):  
Qiuyan Xu ◽  
Zhiyong Liu
Keyword(s):  
Radial Basis Functions ◽  
Radial Function ◽  
Dimensional Space ◽  
Level Set Methods ◽  
Scattered Data ◽  
Surface Modeling ◽  
Basis Functions ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Radial Basis

Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation effect, this is often accompanied by an ill-conditioned algebraic system. The exceedingly large condition number of the discrete matrix makes the numerical calculation time consuming. The paper introduces a truncated exponential function, which is radial on arbitrary n-dimensional space R n and has compact support. The truncated exponential radial function is proven strictly positive definite on R n while internal parameter l satisfies l ≥ ⌊ n 2 ⌋ + 1 . The error estimates for scattered data interpolation are obtained via the native space approach. To confirm the efficiency of the truncated exponential radial function approximation, the single level interpolation and multilevel interpolation are used for surface modeling, respectively.

scholarly journals Hybrid Gaussian-cubic radial basis functions for scattered data interpolation

2018 ◽  
Vol 22 (5) ◽  
pp. 1203-1218 ◽  
Author(s):  
Pankaj K. Mishra ◽  
Sankar K. Nath ◽  
Mrinal K. Sen ◽  
Gregory E. Fasshauer
Keyword(s):  
Radial Basis Functions ◽  
Scattered Data ◽  
Basis Functions ◽  
Data Interpolation ◽  
Scattered Data Interpolation ◽  
Radial Basis
Sign in / Sign up

Export Citation Format

Share Document