Experiments on the evaluation of functional ranges using a random interval arithmetic

A software tool using standard and special interval arithmetic operations together with an idea which is developed in the discrete stochastic arithmetic (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 gives 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 both approaches to obtain a smaller but only highly probable interval containing the range of a rational function for given interval data. Various numerical experiments are given.