Manfred Reimer – författare

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 computerscience and geophysics.

Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed.