Radial Basis Functions
In this chapter the RBF mathematical concepts are exposed considering firstly the interpolation problem with the RBF function defined by known values at source points; a first hands-on example is provided showing how RBF work. Further topics of RBF theory are then introduced considering the differentiation of RBF, the fitting of an RBF with known values at locations different from the source points, the use of regression instead of exact interpolation and finally the management of noisy datasets. The chapter contents will not provide the details of mathematical theory but they will be mainly focused on the relevant results suitable for a wise and aware practical application of RBF.
- Carr JC, Beatson R, Cherri J, Mitchell T, Fright W, McCallum B (2001) Reconstruction and representation of 3D objects with radial basis functions. In: Proceedings of the 28th annual conference on computer graphics and interactive techniques, Los Angeles, CA, pp 67–76Google Scholar
- Press WH, Flannery BP, Teukolsky SA (1992) Numerical recipes in C. The art of scientific computing, 2nd edn. ISBN 0-521-43108-5Google Scholar
- Wendland H (1995) Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. Adv Comput Math 4(1):389–396. ISSN 1019-7168Google Scholar