Reliable Computing

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

Interval Computation of Viswanath's Constant

  • Jaão Batista Oliveira
  • Luiz Henrique De Figueiredo


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.


Mathematical Modeling Computational Mathematic Industrial Mathematic Computer Calculation Interval Arithmetic 
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    Van Iwaarden, R.: RV Interval, a C ++ Interval Arithmetic Package, available at Scholar
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    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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