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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 functions The book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computerscience and geophysics.

Nineteen 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. 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.

These are the Proceedings of the 3rd International Conference on Multivariate Approximation, which was held at Witten-Bommerholz from September 27 until October 2, 1998. The contributions consist of elaborations and extensions of the main results presented during the conference. The following topics are covered: Node Distributions on the Sphere, Positive Quadratures, Discrepancy and Spherical Designs, Fekete Points, Interpolation and Hyperinterpolation on the Sphere, Modelling of Geopotential Data, Periodic, Monotone and Convex Approximations, Stability of the Fast Fourier Transform, Interpolation with Bivariate Splines and Periodic Functions, Range Restricted Interpolation, Saturation Phenomena for Box Spline Operators, Universal Harmonic Functions, Best One-Sided Approximation by Harmonic and Blending Functions, Besov Regularity for the Stokes Problem, Spherical Polynomial Approximations, Simultaneous Approximation in the Dirichlet Space, Weighted K-Functionals and Moduli of Smoothness.

This is a presentation of the main results of the 2nd International Conference on Multivariate Approximation, held at Witten–Bommerholz, September 29 to October 4, 1996. There are contributions to the following Interpolation and Hyper–interpolation on the Sphere, Quadrature, Discrepancy and Spherical Designs, Multivariate Convex Spline Interpolation, Triangular Finite Element Spaces, Polar Form of Splines, Refinable Spline Pairs, Local Box Dimension of Fractal Functions, Symbolic Treatment of Algebraic Systems, Harmonic Approximation and Boundary Behaviour, Quasi–Balayage, Landau–Kolmogorov Inequality, Trigonometric Approximation in Multivariate Periodic Hilbert Spaces, Orthonormal Polynomial Bases of Low Degree, Synthesis and Analysis with Multivariate Wavelets and Frames.