Asymptotic directions for best approximations of \(n\)-dimensional linear forms
type: Item
instance of: scholarly article
title: Asymptotic directions for best approximations of \(n\)-dimensional linear forms
zbMATH Open document ID: 1111.11036
published in: Mathematical Notes
publication date: 2007-03-09T00:00:00Z
review text: For \(\alpha \) in Euclidean \(n\)-space let \({\mathcal L}_{\alpha }: x \mapsto (x,\alpha )\) denote the linear form induced by \(\alpha \). An integral vector \(m\in {\mathbb Z}^n\) is called a \textit{best approximation} (resp. \textit{one-sided best approximation}) of \({\mathcal L}_{\alpha }\), if \(L_{\alpha }(m)\) minimizes the distance to \({\mathbb Z}\) (resp. the fractional part) on the set of integral vectors of smaller norm. These definitions depend on the choice of an arbitrary fixed norm determined by a convex radially symmetric function. The paper investigates the asymptotic behaviour of the one-sided best approximations.
reviewed by: Gabriele Nebe
Mathematics Subject Classification ID: 11J13
Mathematics Subject Classification ID: 11H50
zbMATH DE Number: 5132499
zbMATH Keywords: asymptotic directions of best approximations
zbMATH Keywords: f-best approximation of a linear form
author: Oleg N. German
MaRDI profile type: Publication
full work available at URL: b:matn.0000015021.87265.d9
OpenAlex ID: W2070817067
DOI: 10.1023/B:MATN.0000015021.87265.D9
description: scientific article; zbMATH DE number 5132499