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Constructing lattice bases by means of approximations

  • The construction of a basis of a certain lattice of interest is a basic tool in many fields of algorithmic number theory. All too often we can not compute with the original lattices because of irrational numbers involved but have to work with approximations of them. While helpful bounds were shown about the reduction of lattice bases in cite{buchmann94reducing}, here we introduce the notion of a $(epsilon,delta)$-constructable basis of a lattice and determine the precision of vectors that is necessary to extend a set to a $(epsilon,delta)$-constructable basis.

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Metadaten
Author:Christoph Thiel
Fachbereich/Einrichtung:Hochschule Düsseldorf / Fachbereich - Medien
Document Type:Workingpaper / Report
Year of Completion:2009
Language of Publication:English
Place of publication:Düsseldorf
Title Additional (English):Constructing lattice bases by means of approximations
URN:urn:nbn:de:hbz:due62-opus-6128
Tag:Approximation; FHD; Gitter; Zahlentheorie
approximation; lattices; number theorie
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):Es gilt das deutsche Urheberrecht
Release Date:2010/02/16
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