Backward error analysis

Summary

Backward error analysis studies a computed answer by asking for which nearby input it is the exact answer. The size of that input change is the backward error. The error of the answer, the forward error, is then bounded by about the condition number times the backward error. This splits the analysis into a property of the algorithm (small backward error, that is, numerical stability) and a property of the problem (its conditioning). It was developed and made systematic by James H. Wilkinson in his work on numerical linear algebra.