Certificate — 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 negative curvature — the same set of essays touches all of them, so they are one junction rather than several.
Deciding that a zero has arrived
The previous tolerances were offers — accept this much error, save this much work. A detection threshold is not an offer, because both directions are failures. One matrix here has three genuinely near-invariant subspaces, and the constant somebody typed decides which of them the recurrence stops at; at eight significand bits the same kind of constant produces a proof of something false.
The division that cannot be done
Conjugate gradients divides by pᵀAp at every step, and on a matrix that is not positive definite that number can be zero or negative. This site has guarded against it since its first commit and described it as a failure. In the method that made conjugate gradients famous it is the single most valuable object the iteration can produce, and it costs six matrix–vector products.
Named alongside it
The objects these essays reach for when they reach for this one.
Krylov subspaceNegative curvatureBackward errorCholeskyConjugate gradientsCounterexampleEigenvaluesHalf precisionIndefinite matrixInfinite eigenvalueInvariant subspaceMachine epsilon