Operator complexity — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
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.
Aggregating what the matrix calls strong
The depth phase measured every method it had on the 45°-rotated anisotropic operator — 0.784, 0.883, 0.844 — and diagnosed the failure as being in the discretisation rather than in the hierarchy. Smoothed aggregation is the standard answer to anisotropy. It returns 0.789.
Named alongside it
The objects these essays reach for when they reach for this one.
Algebraic multigridRotated anisotropyStrength of connectionAnisotropyCoarse fine splittingFill-inGalerkin coarse operatorGraph laplacianGrid complexityInterpolation weightsNear null spaceSmoothed aggregation