= Full multigrid
Full multigrid solves first on a coarse mesh, interpolates that approximation to the next finer mesh, and applies a fixed number of <geometric multigrid V-cycles> before proceeding to the next level. If interpolation introduces only the expected discretization-scale error and the cycle count reduces the inherited error sufficiently at every level, the final algebraic error matches the fine-grid discretization error. The geometric sum of level costs is then $O(N)$, unlike reducing an arbitrary fine-grid initial error by an arbitrarily small tolerance.
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