On Optimal Backward Perturbation Bounds

摘要

In general, a computed solution to a problem solves many perturbed problems. the optimal backward perturbation bound for the problem with respect to the computed solution is a measure of the nearness between the perturbed problems and the original problem. An explicit expression of the optimal backward perturbation bound may provide a convenient way of testing the stability of practical algorithms. This paper surveys some new results on optimal backward perturbation bounds for linear systems, underdetermined systems, and linear least squares problems.