Some similarities between multiresolution (wavelet) analysis [see \textit{B. Glowinski}, \textit{W. Lawton}, \textit{M. Ravachol} and \textit{E. Tedenbaum}. Wavelet solution of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension, in computing methods in applied sciences and enginneering, Society for Industrial and Applied Mathematics, Philadelphia, PA, 55-120 (1990)] and multigrid methods are considered for an elliptic boundary value problem. The problem is posed on (or projected to) a finite dimensional space \(V_ 0\) which represents the highest level of resolution that is desired. In a multigrid setting \(V_ 0\) corresponds to \(\Omega^ h\), the space of fine grid vectors. Multigrid with piecewise linear interpolation produces the same orthogonal decomposition of the fine grid \(\Omega^ h\) that multiresolution produces for the space \(V_ 0\). Multigrid formulations use simple, near-orthogonal basis functions that still allow an orthogonal decomposition of the fine grid space.