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Reliable Computing

, Volume 12, Issue 5, pp 365–369 | Cite as

Towards Optimal Use of Multi-Precision Arithmetic: A Remark

  • Vladik Kreinovich
  • Siegfried Rump
Article

Abstract

If standard-precision computations do not lead to the desired accuracy, then it is reasonable to increase precision until we reach this accuracy. What is the optimal way of increasing precision? One possibility is to choose a constant q > 1, so that if the precision which requires the time t did not lead to a success, we select the next precision that requires time q ˙ t˙ It was shown that among such strategies, the optimal (worst-case) overhead is attained when q = 2. In this paper, we show that this “time-doubling” strategy is optimal among all possible strategies, not only among the ones in which we always increase time by a constant q > 1.

Keywords

Interval Arithmetic Longe Computation Time Reliable Computing Short Plan Multiple Precision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Pousse, L., Hanrot, G., Lefevre, V., Pelissier, P., and Zimmermann, P.: MPFR, A Multiple- Precision Binary Floating-Point Library with Correct Rounding, 1'Institut National de Recherche en Informatique et en Automatique INRIA, Technical Report RR-5753, 2005, http://hal.inria.fr/inria-00000818.
  2. 2.
    Revol, N.: MPFI, a Multiple Precision Interval Arithmetic Library, 2001–04, http://perso.ens-lyon.fr/nathalie.revol/mpfi.html.
  3. 3.
    Rump, S. M.: Kleine Fehlerschmnken bei Matrixproblemen, PhD thesis, Universitat Karlsruhe, 1980.Google Scholar
  4. 4.
    Trejo, R. A., Galloway, J., Sachar, C., Kreinovich, V., Baral, C., and Tuan, L. C.: From Planning to Searching for the Shortest Plan: An Optimal Transition, International Journal of Uncertainty, Fuzziness, Knowledge-Based Systems (IJUFKS) 9 (6) (2001), pp. 827–838.MATHGoogle Scholar
  5. 5.
    van der Hoeven, J.: Computations with Effective Real Numbers, Theoretical Computer Science (to appear).Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA
  2. 2.Institute for Reliable ComputingHamburg University of TechnologyHamburgGermany
  3. 3.Faculty of Science and EngineeringWaseda UniversityShinjuku-kuJapan

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