# Interval Computation of Viswanath's Constant

Interval Computation of Viswanath's Constant 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Interval Computation of Viswanath's Constant

, Volume 8 (2) – Oct 21, 2004
8 pages
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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2002 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1014702122205
Publisher site
See Article on Publisher Site

### 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.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 21, 2004

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