Abstract
Viswanath has shown that the terms of the random Fibonacci sequences defined by t 1 = t 2 = 1, and t n−1 ± t n−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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Viswanath, D.: Random Fibonacci Sequences and the Number 1.13198824..., Math. Comp. 69 (231) (2000), pp. 1131–1155.
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Oliveira, J.B., De Figueiredo, L.H. Interval Computation of Viswanath's Constant. Reliable Computing 8, 131–138 (2002). https://doi.org/10.1023/A:1014702122205
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DOI: https://doi.org/10.1023/A:1014702122205