stability

Whether an algorithm keeps small round-off errors from growing out of control as it runs -- a property of the algorithm, not of the problem it's solving.

An algorithm is stable if small errors introduced at any stage (round-off, an imprecise input) do not grow uncontrollably as the computation proceeds, and unstable if such errors can be amplified without bound. Stability is a property of the algorithm applied to a problem, distinct from whether the problem itself is well- or ill-conditioned -- a well-conditioned problem can still be solved by an unstable algorithm, and an ill-conditioned problem cannot be rescued by any algorithm, however stable.

Examples

Gaussian elimination WITHOUT partial pivoting is an unstable algorithm even on a well-conditioned system, since a tiny pivot can amplify round-off without bound.