Preprint A79/2001
Interval computation of Viswanath's constant
Luiz Henrique de Figueiredo | Oliveira, João Batista
Viswanath has shown that the terms of the random Fibonacci sequences defined by $t_1=t_2=1$, and $t_n = \pm t_{n-1} \pm t_{n-2}$ for $n>2$, where each $\pm$~sign is chosen randomly, increase exponentially in the sense that $\sqrt[n]{\abs{t_n}} \rightarrow 1.13198824\ldots$ as $n \rightarrow\infty$ 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.