Radial Basis Function Approximations: Comparison and Applications
For engineers dealing with scattered data in high dimensions, this work provides a comparative analysis of RBF methods, but the results are incremental and lack concrete numerical improvements.
This paper compares several Radial Basis Function (RBF) approximation methods for scattered data, showing that the proposed RBF approach offers lower memory requirements and better approximation quality.
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher dimension d>2, because the other methods require the conversion of a scattered dataset to an ordered dataset (i.e. a semi-regular mesh is obtained by using some tessellation techniques), which is computationally expensive. The RBF approximation is non-separable, as it is based on the distance between two points. This method leads to a solution of Linear System of Equations (LSE) Ac=h. In this paper several RBF approximation methods are briefly introduced and a comparison of those is made with respect to the stability and accuracy of computation. The proposed RBF approximation offers lower memory requirements and better quality of approximation.