3 research outputs found
RBF Interpolation with CSRBF of Large Data Sets
This contribution presents a new analysis of properties of the interpolation
using Radial Bases Functions (RBF) related to large data sets interpolation.
The RBF application is convenient method for scattered d-dimensional
interpolation. The RBF methods lead to a solution of linear system of equations
and computational complexity of solution is nearly independent of a
dimensionality. However, the RBF methods are usually applied for small data
sets with a small span geometric coordinates. This contribution explores
properties of the RBF interpolation for large data sets and large span of
geometric coordinates of the given data sets with regard to expectable
numerical stability of computation
A New Radial Basis Function Approximation with Reproduction
Approximation of scattered geometric 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 method is
useful for a higher dimension d>=2, because the other methods require a
conversion of a scattered dataset to a semi-regular mesh using some
tessellation techniques, which is computationally expensive. The RBF
approximation is non-separable, as it is based on a distance of two points. It
leads to a solution of overdetermined Linear System of Equations (LSE). In this
paper a new RBF approximation method is derived and presented. The presented
approach is applicable for d dimensional cases in general
Radial Basis Function Approximations: Comparison and Applications
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