Numerical Linear Algebra
where the algebra stops being the arithmetic
Concept

Interpolation weights — where it appears

The numbers a coarse correction is spread over the fine unknowns with, and the place a hierarchy's quality is mostly decided.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

the grid the operator came froman edge is a coupling the matrix calls strongkeptinterpolatedwhat the entries decidedcoupling ratio, x against y0.001strong couplings across x0strong couplings along y110rows kept or dropped whole1111×11 grid, θ = 0.25the coarse grid, from the matrix alone

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.

iterative · algebraic multigrid 75 aggregates over 225 unknownsthe matrix chose thismean extent along y3mean extent along x1points adopted by pass two15no coordinate enters the methodand the shape follows the coupling

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.

iterative · anisotropy

Named alongside it

The objects these essays reach for when they reach for this one.

Algebraic multigridAnisotropyStrength of connectionCoarse fine splittingGalerkin coarse operatorM matrixNear null spaceOperator complexityProlongationRotated anisotropySemi coarseningSmoothed aggregation

All concepts