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Robustness and Randomness

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Reliable Implementation of Real Number Algorithms: Theory and Practice

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5045))

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Abstract

The study of robustness problems for computational geometry algorithms is a topic that has been subject to intensive research efforts from both computer science and mathematics communities. Robustness problems are caused by the lack of precision in computations involving floating-point instead of real numbers. This paper reviews methods dealing with robustness and inaccuracy problems. It discusses approaches based on exact arithmetic, interval arithmetic and probabilistic methods. The paper investigates the possibility to use randomness at certain levels of reasoning to make geometric constructions more robust.

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Authors and Affiliations

  1. LE2I UMR CNRS 5158, UFR Sciences, Université de Bourgogne, BP 47870, 21078, Dijon Cedex, France

    Dominique Michelucci & Sebti Foufou

  2. LIRIS UMR 5205, Nautibus, Université Claude Bernard Lyon 1, 46 Bd du 11 Nov. 1918, 69622, Villeurbanne, France

    Jean Michel Moreau

Authors
  1. Dominique Michelucci
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  2. Jean Michel Moreau
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  3. Sebti Foufou
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Peter Hertling Christoph M. Hoffmann Wolfram Luther Nathalie Revol

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Michelucci, D., Moreau, J.M., Foufou, S. (2008). Robustness and Randomness. In: Hertling, P., Hoffmann, C.M., Luther, W., Revol, N. (eds) Reliable Implementation of Real Number Algorithms: Theory and Practice. Lecture Notes in Computer Science, vol 5045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85521-7_8

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  • DOI: https://doi.org/10.1007/978-3-540-85521-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85520-0

  • Online ISBN: 978-3-540-85521-7

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