Year: 2013
Type: preprint
Abstract: We discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to $d$ real numbers $α_1,\ldots,α_d$. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically LLL-reduce a quadratic form with parameter $t$ as $t\downarrow0$. The new idea in this paper is that checking the LLL-conditions consists of solving linear equations in $t$.
Source: arXiv (Cornell University)
Author: Beukers, Frits
Institution: Utrecht University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951715249