Book contents
- Frontmatter
- Contents
- 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: some essentials on Fourier transforms
- Commentary on the Bibliography
- Bibliography
- Index
Preface
Published online by Cambridge University Press: 14 August 2009
- Frontmatter
- Contents
- 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: some essentials on Fourier transforms
- Commentary on the Bibliography
- Bibliography
- Index
Summary
The radial basis function method for multivariate approximation is one of the most often applied approaches in modern approximation theory when the task is to approximate scattered data in several dimensions. Its development has lasted for about 25 years now and has accelerated fast during the last 10 years or so. It is now in order to step back and summarise the basic results comprehensively, so as to make them accessible to general audiences of mathematicians, engineers and scientists alike.
This is the main purpose of this book which aims to have included all necessary material to give a complete introduction into the theory and applications of radial basis functions and also has several of the more recent results included. Therefore it should also be suitable as a reference book to more experienced approximation theorists, although no specialised knowledge of the field is required. A basic mathematical education, preferably with a slight slant towards analysis in multiple dimensions, and an interest in multivariate approximation methods will be suitable for reading and hopefully enjoying this book.
Any monograph of this type should be self-contained and motivated and need not much further advance explanations, and this one is no exception to this rule.
- Type
- Chapter
- Information
- Radial Basis FunctionsTheory and Implementations, pp. ix - xPublisher: Cambridge University PressPrint publication year: 2003