A probabilistic round-off error propagation model. Application to the eigenvalue problem
Francise Chatelin, Marie Christine Brunet · 1990
Abstract It is often assumed that round-off error propagation is a statistical phenomenon, but relatively few studies have been carried out to test the validity of this assumption, and, if proved valid, to extract quantified information for the control of this error propagation. We propose a probabilistic model for round-off propagation which relies on two basic assumptions. The main result is that if the solution depends analytically on a perturbation of the problem, then for a large class of stable algorithms one can compute a confidence interval around the computed solution which contains the exact solution up to a given probability.