Interval computation of Viswanath's constant

Abstract

Viswanath has shown that the terms of the random Fibonacci sequences defined by t1 = t2 = 1, and tn = ± tn-1 ± tn-2 for n > 2, where each ± sign is chosen randomly, increase exponentially in the sense that n√|tn| → 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.