, Volume 8, Issue 2, pp 131-138

Interval Computation of Viswanath's Constant

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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.