A course in approximation theory / Ward Cheney, Will Light

Originally published: Pacific Grove : Brooks/Cole Pub. Company, c2000

Includes bibliographical references (pages 327-354) and indexes

Contents Ch. 1 Introductory Discussion of Interpolation Ch. 2 Linear Interpolation Operators Ch. 3 Optimization of the Lagrange Operator Ch. 4 Multivariate Polynomials Ch. 5 Moving the Nodes Ch. 6 Projections Ch. 7 Tensor-Product Interpolation Ch. 8 The Boolean Algebra of Projections Ch. 9 The Newton Paradigm for Interpolation Ch. 10 The Lagrange Paradigm for Interpolation Ch. 11 Interpolation by Translates of a Single Function Ch. 12 Positive Definite Functions Ch. 13 Strictly Positive Definite Functions Ch. 14 Completely Monotone Functions Ch. 15 The Schoenberg Interpolation Theorem Ch. 16 The Micchelli Interpolation Theorem Ch. 17 Positive Definite Functions on Spheres Ch. 18 Approximation by Positive Definite Functions Ch. 19 Approximate Reconstruction of Functions and Tomography Ch. 20 Approximation by Convolution Ch. 21 The Good Kernels Ch. 22 Ridge Functions Ch. 23 Ridge Function Approximation via Convolutions Ch. 24 Density of Ridge Functions Ch. 25 Artificial Neural Networks Ch. 26 Chebyshev Centers Ch. 27 Optimal Reconstruction of Functions Ch. 28 Algorithmic Orthogonal Projections Ch. 29 Cardinal B-Splines and the Sinc Function Ch. 30 The Golomb-Weinberger Theory Ch. 31 Hilbert Function Spaces and Reproducing Kernels Ch. 32 Spherical Thin-Plate Splines Ch. 33 Box Splines Ch. 34 Wavelets, I Ch. 35 Wavelets, II Ch. 36 Quasi-Interpolation Bibliography Index Index of Symbols