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Radial basis functions
Applications
Contents of the book
Summary of methods and applications
Invertibility of interpolation matrices
Convergence analysis
Interpolation and convergence
Applications to PDEs
General methods for approximation and interpolation
Polynomial schemes
Piecewise polynomials
General nonpolynomial methods
Radial basis function approximation on infinite grids
Existence of interpolants
Convergence analysis
Numerical properties of the interpolation linear system
Convergence with respect to parameters in the radial functions
Radial basis functions on scattered data
Nonsingularity of interpolation matrices
Convergence analysis
Norm estimates and condition numbers of interpolation matrices
Radial basis functions with compact support
Wendland’s functions
Another class of radial basis functions with compact support
Convergence
A unified class
Implementations
The BFGP algorithm and the new Krylov method
The fast multipole algorithm
Preconditioning techniques
Least squares methods
Introduction to least squares
Approximation order results
Discrete least squares
Implementations
Neural network applications
Wavelet methods with radial basis functions
Introduction to wavelets and prewavelets
Basic definitions and constructions
Multiresolution analysis and refinement
Special constructions
Further results and open problems
Further results
Open problems