Bisection — where it appears
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
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.
An eigenvalue count that cannot be slightly wrong
Every spectral computation on this site returns floats with errors in them. Counting eigenvalues below a shift by the signs of an unpivoted elimination returns an integer, and an integer cannot be 6.9999999997 — so the answer is exactly right, or wrong by a whole eigenvalue, and where the second happens is a band of measurable width.
Named alongside it
The objects these essays reach for when they reach for this one.
Exact ground truthBranch and boundCondition numberEigenvalue bracketExistence and uniquenessInertiaInterval arithmeticKrawczyk operatorLDLᵀ factorisationNumerical rankPruningRoot finding