Stability and Accuracy (numerical analysis)

Definition

Stability refers to the effects of computational error on the result computed by an algorithm. An algorithm is stable if the result it produces is relatively insensitive to perturbations due to approximations made during the computation.

In other words, how sensitive the computed solution is to small perturbations introduced by the algorithm. (ie. truncations, rounding, approximations). Stability is about the algorithm.

Accuracy refers to the closeness of the computed solution to the true solution. Just because an algorithm is stable, doesn't mean that the computed solution is accurate. Accuracy depends on both conditioning and stability.

Stability tells us that the solution obtained is exact for a nearby problem, but the solution to that nearby problem is not necessarily close to the solution to the original problem if the problem unless the problem is well-conditioned. right algorithm, wrong problem: stable, ill-conditioned wrong algorithm, right problem: unstable, well-conditioned

References

"What is conditioning?" - Sensitivity and Conditioning (numerical analysis)