ABSTRACT
In this chapter, we summarize the basic features of local Fourier analysis for multigrid methods without going into technical details. It is intended to give a short overview about the main ideas, the power, and the range of applicability of local Fourier analysis. In this respect it should be particularly worthwhile for the practitioner who is mainly interested in the accompanying software. Here he gets a qualitative insight into the principles of local Fourier analysis without wading through the theoretical chapters from the second part of this monograph. Moreover, for the theoretically oriented researcher it may serve as a preparation and guideline for the (more technical) description of local Fourier analysis for multigrid presented in the second part.
