Review on stochastic approach to round-off error analysis and its applications

Because of round-off error propagation in floating-point arithmetic, any result provided by a computer always contains an error. The Permutation-Perturbation method, also known under the CESTAC (Controle et Estimation Stochastique des Arrondis de Calcul) method is a precious tool: (i) for evaluating the accuracy of results provided by direct algorithms performed by a computer, (ii) for breaking off correctly any iterative process, and for evaluating the accuracy of the results, and (iii) for determining the optimal step or the optimal mesh in the approximate algorithms. A review of this method and of these applications is presented in this paper.