Year: 2005
Type: preprint
Abstract: In this article, we prove the existence and uniqueness of a certain distribution function on the unit interval. This distribution appears in Brent's model of the analysis of the binary gcd algorithm. The existence and uniqueness of such a function has been conjectured by Richard Brent in his original paper \cite{brent}. Donald Knuth also supposes its existence in \cite{knuth} where developments of its properties lead to very good estimates in relation with the algorithm. We settle here the question of existence, giving a basis to these results, and study the relationship between this limiting function and the {\it binary Euclidean operator} $B_2$, proving rigorously that its derivative is a fixed point of $B_2$.
Source: arXiv (Cornell University)
Author: Maze, Gerard
Institution: University of Zurich
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950608310