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 computer science and geophysics.

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Contributions by H. Albrecher/J. Hartinger/R.F. Tichy, J.S. Brauchart, M. Charina/C. Conti, C.K. Chui/Q. Jiang, D.P. Dryanov, N. Dyn/D. Levin/A. Luzzatto, K. Dziedziul/K. Jetter, A. Iske, L. Karp/H.S. Shapiro, A. Kunoth, A. Le Méhauté, G. Nürnberger/F. Zeilfelder, G. Plonka/M. Tasche, M. Reimer, P. Sablonnière, T. Sauer, H. Wendland, G. Zimmermann.