Topics in Multivariate Approximation and Interpolation

This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry.

A collection of articles of highest scientific standardAn excellent introduction and overview of recent topics from multivariate approximationA valuable source of references for specialists in the fieldA representation of the state-of-the-art in selected areas of multivariate approximationA rigorous mathematical introduction to special topics of interdisciplinary research

1. Durrmeyer Operators and Their Natural Quasi-Interpolants (E. Berdysheva, K. Jetter and J. Stöckler)
2. Three Families of Nonlinear Subdivision Schemes (N. Dyn)
3. Parameterization for Curve Interpolation (M.S. Floater and T. Surazhsky)
4. Refinable Multivariate Spline Functions (T. Goodman and D. Hardin)
5. Adaptive Wavelets for Sparse Representations of Scattered Data (A. Kunoth)
6. Ready-to-Blossom Bases in Chebyshev Spaces (M-L. Mazure)
7. Structural Analysis of Subdivision Surfaces - A Summary (U. Reif and J. Peters)
8. Polynomial Interpolation in Several Variables: Lattices, Differences and Ideals (T. Sauer)
9. Computational Aspects of Radial Basis Function Approximation (H. Wendland)
10. Learning Theory: From Regression to Classification (Q. Wu, Y. Ying and D-X. Zhou)
11. Coherent States from Nonunitary Representations (G. Zimmermann)