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.

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