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. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
cestac method monte carlo methods interval analysis directed interval analysis stochastic methods for error evaluation functional range evaluation