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Testing Stochastic Arithmetic and CESTAC Method Via Polynomial Computation

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Foundations of Fuzzy Logic and Soft Computing (IFSA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4529))

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Abstract

The CESTAC method and its implementation known as CADNA software have been created to estimate the accuracy of the solution of real life problems when these solutions are obtained from numerical methods implemented on a computer. The method takes into account uncertainties on data and round-off errors. On another hand a theoretical model for this method in which operands are gaussian variables called stochastic numbers has been developed. In this paper numerical examples based on the Lagrange polynomial interpolation and polynomial computation have been constructed in order to demonstrate the consistency between the CESTAC method and the theory of stochastic numbers. Comparisons with the interval approach are visualized.

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Author information

Authors and Affiliations

  1. CNRS, UMR 7606, LIP6,University Pierre et Marie Curie, 4 place Jussieu, 75252 Paris cedex 05, France

    René Alt & Jean-Luc Lamotte

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, “Acad. G. Bonchev” st., bl. 8, 1113 Sofia, Bulgaria

    Svetoslav Markov

Authors
  1. René Alt
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  2. Jean-Luc Lamotte
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  3. Svetoslav Markov
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Editor information

Patricia Melin Oscar Castillo Luis T. Aguilar Janusz Kacprzyk Witold Pedrycz

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Alt, R., Lamotte, JL., Markov, S. (2007). Testing Stochastic Arithmetic and CESTAC Method Via Polynomial Computation. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_2

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  • DOI: https://doi.org/10.1007/978-3-540-72950-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72917-4

  • Online ISBN: 978-3-540-72950-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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