Experiments with data perturbations to study condition numbers and numerical stability

Ill-conditioning as well as roundoff errors lead to inaccuracies in scientific applications. Random perturbations in the initial data allow to derive an error estimation. By varying the size of these perturbations and under some reasonable assumption on the rounding errors, we can find an interval of perturbations where a log-linear least-squares fit gives an estimation of the regularity and the condition number of the problem.