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Reply to "Backward Error Analysis ..."

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44766

Kettner,  Lutz
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45191

Pion,  Sylvain
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45391

Schirra,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45771

Yap,  Chee
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Zitation

Kettner, L., Mehlhorn, K., Pion, S., Schirra, S., & Yap, C. (2006). Reply to "Backward Error Analysis.." In Computational Science and Its Applications - ICCSA 2006, I (pp. 60-60). Berlin, Germany: Springer.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-23DB-8
Zusammenfassung
The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause implementations to fail. Although this is well known, it is not common knowledge. There is no paper that systematically discusses what can go wrong and provides simple examples for the di.erent ways in which floating-point implementations can fail. Due to this lack of examples, instructors of computational geometry have little material for demonstrating the inadequacy of floating-point arithmetic for geometric computations, students of computational geometry and implementers of geometric algorithms still underestimate the seriousness of the problem, and researchers in our and neighboring disciplines still believe that simple approaches are able to overcome the problem. In this paper, we study simple algorithms for two simple geometric problems, namely computing convex hulls and triangulations of point sets, and show how they can fail and explain why they fail when executed with floating-point arithmetic.