Radial Basis Functions
Theory and Implementations

A comprehensive bibliography rounds off what will prove a very valuable work.

Martin D. Buhmann (Author)

9780521101332, Cambridge University Press

Paperback / softback, published 12 February 2009

272 pages
22.9 x 15.2 x 1.6 cm, 0.4 kg

"A must read for anyone making direct use of this tool, and a must browse for anyone interested in keeping up with the state of the art in multivariate approximation theory in general." Computing Reviews

In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a powerful tool which work well in very general circumstances and so are becoming of widespread use as the limitations of other methods, such as least squares, polynomial interpolation or wavelet-based, become apparent. The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence. A comprehensive bibliography rounds off what will prove a very valuable work.

Preface
1. Introduction
2. Summary of methods and applications
3. General methods for approximation and interpolation
4. Radial basis function approximation on infinite grids
5. Radial basis functions on scattered data
6. Radial basis functions with compact support
7. Implementations
8. Least squares methods
9. Wavelet methods with radial basis functions
10. Further results and open problems
Appendix
Bibliography
Index.

Subject Areas: Numerical analysis [PBKS]