Concept
Preconditioning — where it appears
2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
The rate the condition number predicts
Conjugate gradients converge at a rate governed by the square root of the condition number. That is a bound rather than an estimate, it is provable, and it is loose enough that provisioning iterations from it wastes nine out of ten.
Changing the condition number on purpose
Preconditioning is usually introduced as a trick that makes an iteration converge faster. It is not a trick. It is solving a different system with the same solution and a condition number chosen rather than inherited, and the new condition number is computable.
Named alongside it
The objects these essays reach for when they reach for this one.
Condition numberConjugate gradientsJacobi iterationSparsityCholeskyConvergence rateFill-inIncomplete choleskyKrylov subspaceModel problemOrthogonalityResidual