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Asymptotic Probabilistic Analysis of an Algorithm for Addition Subtraction Chains

  • Raúl Gouet
  • Jorge Olivos

Abstract

The efficient computation of integer powers of real numbers is an old challenging problem. A good introduction to the subject, can be found in Knuth (1980), pages 441–462.

Keywords

Markov Chain Wiener Process Invariance Principle Binary Representation Binary Method 
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. Knuth D. Seminumerical Algorithms. The Art of Computer Programming. Vol II. Addison Wesley (1980).Google Scholar
  2. Gonnet G. H., Baeza-Yates R. Handbook of Algorithms, 2nd Ed., Addison Wesley (1991).Google Scholar
  3. F. Morain, J. Olivos. Speeding up the Computations on an Elliptic Curve using Addition-Subtraction Chains. Theoretical Informatics and Applications. Vol. 24, num. 6, 1990, pp. 531–543.MathSciNetzbMATHGoogle Scholar
  4. Billingsley P. Convergence of Probability Measures. Wiley (1968).Google Scholar
  5. Dacunha-Castelle D., Duflo M. Probabilités et Statistiques, vol 2, Problèmes à Temps Mobile. Masson (1983).Google Scholar
  6. Breiman L. Probability. Addison Wesley (1968).Google Scholar
  7. Flajolet Ph., Soria M. Gaussian limiting distributions for the number of components in combinatorial structures. Rapport de Recherche 809, INRIA (1988).Google Scholar
  8. Neveu J. Martingales à Temps Discret. Masson (1972).Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Raúl Gouet
    • 1
  • Jorge Olivos
    • 2
  1. 1.Departamento de Ingeniería MatemáticaChile
  2. 2.Departamento de Ciencias de la ComputaciónFacultad de Ciencias Físicas y MatemáticasSantiagoChile

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