Constructive approximation and numerical methods in geodetic research today - an attempt at a categorization based on an uncertainty principle

Current activities and recent progress on constructive approximation and numerical analysis in physical geodesy are reported upon. Two major topics of interest are focused upon, namely trial systems for purposes of global and local approximation and methods for adequate geodetic application. A fundamental tool is an uncertainty principle, which gives appropriate bounds for the quantification of space and momentum localization of trial functions. The essential outcome is a better understanding of constructive approximation in terms of radial basis functions such as splines and wavelets.