Experiments on the evaluation of functional ranges using a random interval arithmetic |
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| Affiliation: | 1. Department of Mathematics, Imam Khomeini International University, PO Box 288, Gazvin 34194, Iran;2. Department of Mathematics, Islamic Azad University, Tehran Branch, Tehran, Iran;1. Department of Mathematics, Science and Research Branch, Islamic Azad University, PO Box 14515-397, Tehran, Iran;2. Department of Mathematics, Imam Khomeini International University, PO Box 288, Qazvin, Iran;3. Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran;1. Institute of Mathematics and Informatics, Akademijos 4, LT 08663 Vilnius, Lithuania;2. Centre for Process Systems Engineering, Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, UK;1. Institute for Meteorology and Climate Research (IMK-IFU), Forschungszentrum Karlsruhe, Kreuzeckbahnstraße 19, 82467 Garmisch-Partenkirchen, Germany;2. Federal Waterways Engineering and Research Institute, Coastal Department, Wedeler Landstraße 157, 22559 Hamburg, Germany |
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| Abstract: | 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. |
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