For many applications (irregular sampling of band-limited functions, reconstruction from local averages, coorbit theory) one has the idea that the description of a constructive algorithm is enough to claim that one has described a practical tool. However, in most case the necessary steps (building a perfect nearest neighborhood interpolation, projecting perfectly onto the multi-window spline-type space etc.) are NOT REALIZABLE on a computer.

Hence it is necessary to develop/describe concepts which allow to say: Given a (family of) spaces and some (admitted relative) error level eps > 0 one can find a realizable method (something that we can do for example using MATLAB on our notebooks) which does a - up to that given error level for that specific norm - good job on all the elements of the space under consideration.

The idea is to really have a finite implementation for the continuous (multi-dimensional) problem. Doing the (integral transform) FT (Fourier transform) using FFTs is a prototype of such a problem,
or finding dual Gabor atoms using the finite Gabor toolbox (work of N.Kaiblinger) .