Multivariate Approximation and Applications

doi:10.1017/CBO9780511569616

Multivariate approximation theory is today an increasingly active research area. It encompasses a wide range of tools for multivariate approximation such as multi-dimensional splines and finite elements, shift-invariant spaces and radial-basis functions. Approximation theory in the multivariate setting has many applications including numerical analysis, wavelet analysis, signal processing, geographic information systems, computer aided geometric design and computer graphics. The field is fascinating since much of the mathematics of the classical univariate theory does not straightforwardly generalize to the multivariate setting, so new tools are required. This advanced introduction to multivariate approximation and related topics consists of nine articles written by leading experts surveying many of the new ideas and their applications. Each article introduces a particular topic, takes the reader to the forefront of research and ends with a comprehensive bibliography. This unique account is an ideal introduction to the subject for researchers, in universities and industry, and graduate students.

‘… very useful … every library should have this book.’

Source: Numerical Algorithms

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Multivariate Approximation and Applications

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Contents

Frontmatter
pp i-ii

Contents
pp iii-iv

List of contributors
pp v-vi

Preface
pp vii-x

1 - Characterization and construction of radial basis functions
pp 1-24

2 - Approximation and interpolation with radial functions
pp 25-43

3 - Representing and analyzing scattered data on spheres
pp 44-72

4 - A survey on L2-approximation orders from shift-invariant spaces
pp 73-111

5 - Introduction to shift-invariant spaces. Linear independence
pp 112-151

6 - Theory and algorithms for nonuniform spline wavelets
pp 152-187

7 - Applied and computational aspects of nonlinear wavelet approximation
pp 188-212

8 - Subdivision, multiresolution and the construction of scalable algorithms in computer graphics
pp 213-251

9 - Mathematical methods in reverse engineering
pp 252-284

Index
pp 285-286

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Multivariate Approximation and Applications

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