Wavelets and Multigrid

This note explores the suggestive similarities between wavelet (multiresolution) and multigrid approaches to general operator equations. After presenting the essentials of wavelet and multigrid methods, it can be shown that classical multigrid methods use near-orthogonal basis functions to provide the same orthogonal decomposition of the fine grid space ${\bf \Omega} ^h $ that multiresolution methods generate for the maximum resolution space $V_0 $.