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

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  • Alt, R.
  • Lamotte, J.-L.

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.

Suggested Citation

  • Alt, R. & Lamotte, J.-L., 2001. "Experiments on the evaluation of functional ranges using a random interval arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(1), pages 17-34.
    • Handle: RePEc:eee:matcom:v:56:y:2001:i:1:p:17-34
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    References listed on IDEAS

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    1. Vignes, J., 1978. "New methods for evaluating the validity of the results of mathematical computations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(4), pages 227-249.
    2. Vignes, J., 1988. "Review on stochastic approach to round-off error analysis and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 481-491.
    3. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.
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    Cited by:

    1. Zilinskas, Julius & Bogle, Ian David Lockhart, 2006. "Balanced random interval arithmetic in market model estimation," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1367-1378, December.

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