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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

These proceedings contain the main topics and results presented at the Fourth International Conference on Multivariate Approximation. The meeting took place during the week of September 24-29, 2000 at the now well-known "Haus Bommerholz", the guest-house of the University of Dortmund. It hosted 43 participants from 16 countries, and the program included 9 invited one-hour lectures, 21 contributed talks, and two problem sessions. The articles collected here are carefully peer-refereed and suitably edited for publication. Following the tradition of this series of conferences, the meeting was aimed at advancing selected topics of Multivariate Approximation Theory. These include approximation on compact sets (such as spheres, balls, or compact ho­ mogeneous manifolds), spherical designs and energy functionals, interpolation by radial basis functions and by splines, frame theory and Gabor analysis, re­ finable function systems and subdivision, properties of harmonic, polyharmonic and blending functions, sampling and data compression, among others. The editors would like to express their thanks to all who have given their sup­ port to the conference, and to the preparation of this book. In particular, our thanks go to the Deutsche Forschungsgemeinschaft for their funding of the con­ ference, to the University of Dortmund, and to the staff of Haus Bommerholz for their help running the conference, and to the Universities of Dortmund and Duisburg for the financial support of this proceedings volume.

This volume contains a selection of eighteen peer-reviewed articles that were presented at the 5th International Conference on Multivariate Approximation, held in Witten-Bommerholz in September 2002. The contributions cover recent developments of constructive approximation on manifolds, approximation by splines and kernels, subdivision techniques and wavelet methods. The main topics are:- applications of multivariate approximation in finance- approximation and stable reconstruction of images, data reduction- multivariate splines for Lagrange interpolation and quasi-interpolation- radial basis functions- spherical point sets- refinable function vectors and non-stationary subdivision- applications of adaptive wavelet methods- blending functions and cubature formulae- singularities of harmonic functionsThe book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computer science and geophysics.

This volume presents the main results of the 4th International Conference on Multivariate Approximation, which was held at Witten-Bommerholz, September 24-29, 2000. Nineteen selected, peer-reviewed contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. The book is an essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.

Presents papers from an international workshop on multivariate approximation. Topics discussed include: characterization and creation of wavelet frames; fast algorithms for simultaneous polynomial approximation; and quantitative aspects of wavelet bases in L2.

This volume consists of 24 refereed carefully edited papers on various topics in multivariate approximation. It represents the proceedings of a workshop organized by the University of Firenze, and held in September 1995 in Montecatini, Italy.The main themes of the volume are multiresolution analysis and wavelets, multidimensional interpolation and smoothing, and computer-aided geometric design. A number of particular topics are included, like subdivision algorithms, constrained approximation and shape-preserving algorithms, thin plate splines, radial basis functions, treatment of scattered data, rational surfaces and offsets, blossoming, grid generation, surface reconstruction, algebraic curves and surfaces, and neural networks.