Experiments on the evaluation of functional ranges using a random intervalarithmetic

A software tool using standard and special interval arithmetic operations t ogether with an idea which is developed in the discrete stochastic arithmet ic (DSA) approach for round-off error evaluation is proposed in this paper for a statistical computation of functional ranges. The CESTAC method is a Monte Carlo method which uses DSA and provides the accuracy on any computed result with a high probability. On the other hand, interval computation gi ves a guaranteed interval containing the result but this interval may be in some cases useless because much too wide. Here it is proposed to combine b oth approaches to obtain a smaller but only highly probable interval contai ning the range of a rational function for given interval data. Various nume rical experiments are given. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.