Rotated anisotropy — where it appears
Coarsening in one direction only
Leave the smoother alone and halve only the strong direction, and the smoothing factor is 0.3340 — identical to line relaxation's, at every anisotropy and every weight, to twelve digits. The convergence factors are then a factor of three apart, and at 45° both repairs fail outright.
A hierarchy with no grid behind it
On a graph Laplacian the algebraic V-cycle converges at 0.199 a cycle, its grid complexity is an unremarkable 3.05, and its operator complexity is 17.7 — one level of forty-one unknowns is entirely dense. The number people quote is the one that does not measure the work.
Named alongside it
The objects these essays reach for when they reach for this one.
Algebraic multigridAnisotropyCoarse fine splittingFill-inGalerkin coarse operatorGraph laplacianGrid complexityLine relaxationM matrixOperator complexityProlongationRestriction