Existence and uniqueness — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as krawczyk operator — the same set of essays touches all of them, so they are one junction rather than several.
Proving the answer is in the box
Every other method here computes a number and estimates how wrong it is. This one returns a verdict: there is exactly one solution in this box, or there is none, or — the honest third outcome — nothing can be said. Two of the three are proofs about infinitely many points from finitely many operations.
Where the box is cut
A branch-and-bound with an interval operator settles a whole square — two roots proved unique, forty-two regions proved empty, nothing left undecided, in 87 evaluations. Move the roots so one lands on the first bisection and it proves nothing at all, at any depth. Cutting at 0.485 instead of 0.5 finds both, in a quarter of the work.
Named alongside it
The objects these essays reach for when they reach for this one.
Interval arithmeticKrawczyk operatorBisectionBranch and boundDirected roundingExact ground truthJacobianNewton iterationPruningRoot findingSubdivisionUnit roundoff