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 standard. - An excellent introduction and overview of recent topics from multivariate approximation. - A valuable source of references for specialists in the field. - A representation of the state-of-the-art in selected areas of multivariate approximation. - A rigorous mathematical introduction to special topics of interdisciplinary research.

Preface. -- 1. Durrmeyer Operators and Their Natural Quasi-Interpolants (E. Berdysheva, K. Jetter and J. St̲ckler). -- 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). -- Index.

Includes bibliographical references and index.

Durrmeyer operators and their natural quasi-interpolants -- Three families of nonlinear subdivision schemes -- Parameterization for curve interpolation -- Refinable multivariate spline functions -- Adaptive wavelets for sparse representations of scattered data -- Ready-to-blossom bases in Chebyshev spaces -- Structural analysis of subdivision surfaces-a summary -- Polynomial interpolation in several variables : lattices, differences, and ideals -- Computational aspects of radial basis function approximation -- Learning theory : from regression to classification -- Coherent states from nonunitary representations.

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