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

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.

DIV-CURL WEIGHTED MINIMIZING SPLINES

2007 ◽  
Vol 05 (02) ◽  
pp. 95-122 ◽  
Author(s):  
M. N. BENBOURHIM ◽  
A. BOUHAMIDI
Keyword(s):  
Vector Field ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Approximation Problem ◽  
Scattered Data ◽  
Scalar Function ◽  
Basis Functions ◽  
Thin Plate Splines ◽  
Numerical Examples ◽  
Radial Basis

The paper deals with a div-curl approximation problem by weighted minimizing splines. The weighted minimizing splines are an extension of the well-known thin plate splines and are radial basis functions which allow the approximation or the interpolation of a scalar function from given scattered data. In this paper, we show that the theory of the weighted minimizing splines may also be used for the approximation or for the interpolation of a vector field controlled by the divergence and the curl of the vector field. Numerical examples are given to show the efficiency of this method.

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