Interval computation of Viswanath's constant

Publikationstyp
Journal Article
Date Issued
2001
Sprache
English
Author(s)
Oliveira, João Batista Souza de  
Figueiredo, Luiz Henrique de  
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/9352
Journal
Reliable Computing  
Volume
8
Issue
2
Start Page
131
End Page
138
Citation
Reliable Computing 8 (2): 131-138 (2002-04-01)
Publisher DOI
10.1023/A:1014702122205
Scopus ID
2-s2.0-0036533553
Publisher
Kluwer
Viswanath has shown that the terms of the random Fibonacci sequences defined by t = t = 1, and t = ± t ± t for n > 2, where each ± sign is chosen randomly, increase exponentially in the sense that n√|t | → 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. 1 2 n n-1 n-2 n
DDC Class
004: Informatik
510: Mathematik
More Funding Information
The authors are partially supported by research grants from the Brazilian Council for Scientific and Technological Development (CNPq) and by the summer post-doctoral program at IMPA.