Constrained minimisation — where it appears
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Also named here as saddle-point systems — the same set of essays touches all of them, so they are one junction rather than several.
When symmetry is not enough
The matrix [[0, 1], [1, 0]] is symmetric, nonsingular and perfectly conditioned, and there is no diagonal entry to pivot on. Every factorisation restricted to symmetric interchanges and one-by-one pivots fails on it, at any depth of searching, because every entry it could search is zero. The repair is to take two variables at once.
The formula that was already optimal
Ask for the interpolation that minimises the energy of its own columns and the answer is the classical AMG formula — to zero at every row of the one-dimensional Laplacian, and to four digits in two dimensions. On the operator rotated to 45° the two part company, and the gap between them is a diagnostic that needs no reference solution.
Named alongside it
The objects these essays reach for when they reach for this one.
Saddle-point systemsA normAlgebraic multigridAnisotropyBunch–KaufmanCholeskyCoarse grid correctionComplete pivotingEnergy minimisationGalerkin operatorGrowth factorInterpolation