A wavelet variation of the \Frequency decomposition multigrid method, Part I" (FDMGM) of Hackbusch Numer. Math., 56, pp. 229-245, 1989 ] is presented. The perfect reconstruction property and the multiresolution structure of wavelets yield the robustness of the additive as well as of the multiplicative version of a two-level method corresponding to any intermediate level in the FDMGM. Aspects of...