Existence of a Limiting Distribution for the Binary GCD Algorithm
摘要
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} , proving rigorously that its derivative is a fixed point of .
引用
@article{arxiv.math/0504426,
title = {Existence of a Limiting Distribution for the Binary GCD Algorithm},
author = {Gerard Maze},
journal= {arXiv preprint arXiv:math/0504426},
year = {2010}
}
备注
13 pages. New introduction, conclusion and several typos corrected