Algebraic multigrid — where it appears
Also named here as coarse fine splitting, strength of connection — the same set of essays touches all of them, so they are one junction rather than several.
The coarse grid the matrix chooses
Given a tridiagonal matrix and no information about a grid, the coarsening keeps every other point and derives the weights ½, 1, ½ — the operators the geometric method was handed. Given the anisotropic operator, it discovers semi-coarsening, in the right direction, without a coordinate.
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.
Coarse fine splittingGalerkin coarse operatorStrength of connectionAnisotropyFill-inGraph laplacianGrid complexityInterpolation weightsM matrixOperator complexityProlongationRotated anisotropy