An efficient stochastic method for round-off error analysis

Abstract

This paper presents a survey of research results obtained by the authors and by their team, on the round-off error propagation and the accuracy of mathematical computations. The efficiency of the Permutation-Perturbation method is shown:i)For evaluating the accuracy of the exact finite method results,ii)For breaking off the iterative processes using the optimum termination criterion and evaluating the accuracy of the results,iii)For choosing the optimum integration step in approximate methods, such as the finite difference method. The Permutation-Perturbation method may be also used to evaluate the data error propagation. Examples are presented to illustrate the efficiency of the method.