Stability and Accuracy

$$\left\{\begin{array}{l} \mbox {Stability: used to categori... ... \mbox {Conditioning: categorizes problems} \end{array}\right.$$

Algorithm is stable: small perturbation to input leads to small changes in output backward error analysis $\rightarrow$ stable if the result it produces is the exact solution to a nearby problem.

Accuracy: closeness of computed and true solution.

$$\mbox {Stable} \Rightarrow \mbox {Accurate}$$

Stable $\rightarrow$ output is exact for a nearby problem but solution to nearby problem is not necessarily close to the solution to the original problem UNLESS problem is stable.

$\therefore$ inaccuracy can result from applying a stable algorithm to an ill-conditioned problem as well as from applying an unstable algorithm to a well-conditioned problem.

$\Box$