A Course in Approximation Theory

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Introductory discussion of interpolation
Linear interpolation operators
Optimization of the Lagrange operator
Multivariate polynomials Moving the nodes Projections
Tensor-product interpolation
The Boolean algebra of projections
The Newton paradigm for interpolation
The Lagrange paradigm for interpolation
Interpolation by translates of a single function
Positive definite functions
Strictly positive definite functions
Completely monotone functions
The Schoenberg interpolation theorem
The Micchelli interpolation theorem
Positive definite functions on spheres
Approximation by positive definite functions
Approximate reconstruction of functions and tomography
Approximation by convolution
The good kernels Ridge functions
Ridge function approximation via convolutions
Density of ridge functions
Artificial neural networks
Chebyshev centers Optimal reconstruction of functions
Algorithmic orthogonal projections
Cardinal B-splines and the sinc function
The Golomb-Weinberger theory Hilbert function spaces and reproducing kernels
Spherical thin-plate splines Box splines Wavelets, I Wavelets, II Quasi-interpolation
Bibliography
Index
Index of symbols
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