内容简介：
This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable.
Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions.
An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.
Originally published by Brooks Cole/Cengage Learning as ISBN: 978-0-534-36224-9.
书籍目录：
Contents
Chapter 1
Introductory Discussion of Interpolation 1
Chapter 2
Linear Interpolation Operators 11
Chapter 3
Optimization of the Lagrange Operator 18
Chapter 4
Multivariate Polynomials 25
Chapter 5
Moving the Nodes 32
Chapter 6
Projections 39
Chapter 7
Tensor-Product Interpolation 46
Chapter 8
The Boolean Algebra of Projections 51
Chapter 9
The Newton Paradigm for Interpolation 57
Chapter 10
The Lagrange Paradigm for Interpolation 62
Chapter 11
Interpolation by Translates of a Single Function 71
Chapter 12
Positive Definite Functions 77
Chapter 13
Strictly Positive Definite Functions 87
Chapter 14
Completely Monotone Functions 94
Chapter 15
The Schoenberg Interpolation Theorem 101
Chapter 16
The Micchelli Interpolation Theorem 109
Chapter 17
Positive Definite Functions on Spheres 119
Chapter 18
Approximation by Positive Definite Functions 131
Chapter 19
Approximate Reconstruction of Functions and Tomography 141
Chapter 20
Approximation by Convolution 148
Chapter 21
The Good Kernels 157
Chapter 22
Ridge Functions 165
Chapter 23
Ridge Function Approximation via Convolutions 177
Chapter 24
Density of Ridge Functions 184
Chapter 25
Artificial Neural Networks 18
Chapter 26
Chebyshev Centers 197
Chapter 27
Optimal Reconstruction of Functions 202
Chapter 28
Algorithmic Orthogonal Projections 210
Chapter 29
Cardinal B-Splines and the Sine Function 215
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