Reliable Computing

, Volume 8, Issue 2, pp 131–138 | Cite as

Interval Computation of Viswanath's Constant

  • Jaão Batista Oliveira
  • Luiz Henrique De Figueiredo
Article

Abstract

Viswanath has shown that the terms of the random Fibonacci sequences defined by t1 = t2 = 1, and tn−1 ± tn−2 for n > 2, where each ± sign is chosen randomly, increase exponentially in the sense that \(\sqrt[n]{{\left| {t_n } \right|}}\) → 1.13198824... as n → ∞ with probability 1. Viswanath computed this approximation for this limit with floating-point arithmetic and provided a rounding-error analysis to validate his computer calculation. In this note, we show how to avoid this rounding-error analysis by using interval arithmetic.

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References

  1. 1.
    Graham, R. L., Knuth, D. E., and Patashnik, O.: Concrete Mathematics-A Foundation for Computer Science, Addison-Wesley, Reading, MA, second edition, 1994.Google Scholar
  2. 2.
    Moore, R. E.: Interval Analysis, Prentice Hall, Englewood Cliffs, 1966.Google Scholar
  3. 3.
    Van Iwaarden, R.: RV Interval, a C ++ Interval Arithmetic Package, available at http://www-math.cudenver.edu/~rvan/Software.html.Google Scholar
  4. 4.
    Viswanath, D.: Random Fibonacci Sequences and the Number 1.13198824..., Math. Comp. 69 (231) (2000), pp. 1131–1155.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Jaão Batista Oliveira
    • 1
  • Luiz Henrique De Figueiredo
    • 2
  1. 1.Faculdade de InformáticaPontificia Universidade Católica do Rio Grande do SulPorto Alegre, RSBrazil
  2. 2.IMPA—Instituto de Matemática Pura e AplicadaRio de Janeiro, RJBrazil

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