Scattered Data Approximation

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"Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction to this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity." Since it contains complete proofs it is a perfect textbook for graduate courses on multivariate approximation, and can be used to support courses in computer-aided geometric design and meshless methods for partial differential equations.
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Editorial Reviews

From the Publisher
"Scattered Data Approximation provides the most complete up-to-date reference on multivariate scattered data approximation from an RBF/mesh-free point of view...I would like to close with a high recommendation of this book. It should be part of anyone's library on modern multivariate approximation techniques."
SIAM Review
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Product Details

Meet the Author

Holger Wendland is Associate Professor at the Institute for Numerical and Applied Mathematics at Georg-August-University, Göttingen.

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Table of Contents

1 Applications and motivations 1
2 Haar spaces and multivariate polynomials 18
3 Local polynomial reproduction 24
4 Moving least squares 35
5 Auxiliary tools from analysis and measure theory 46
6 Positive definite functions 64
7 Completely monotone functions 85
8 Conditionally positive definite functions 97
9 Compactly supported functions 119
10 Native spaces 133
11 Error estimates for radial basis function interpolation 172
12 Stability 206
13 Optimal recovery 223
14 Data structures 230
15 Numerical methods 253
16 Generalized interpolation 289
17 Interpolation on spheres and other manifolds 308
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