Conditioning properties of the LLL algorithm

Franklin T LUK; Sanzheng Qiao

doi:10.1117/12.834183

Conditioning properties of the LLL algorithm

Franklin T LUK, Sanzheng Qiao^*

^*Corresponding author for this work

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

2 Citations (Scopus)

Abstract

Although the LLL algorithm1 was originally developed for lattice basis reduction, the method can also be used² to reduce the condition number of a matrix. In this paper, we propose a pivoted LLL algorithm that further improves the conditioning. Our experimental results demonstrate that this pivoting scheme works well in practice.

Original language	English
Title of host publication	Mathematics for Signal and Information Processing
Editors	Mark S. Schmalz
DOIs	https://doi.org/10.1117/12.834183
Publication status	Published - 2009
Event	Mathematics for Signal and Information Processing - San Diego, CA, United States Duration: 2 Aug 2009 → 5 Aug 2009

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	7444
ISSN (Print)	0277-786X

Conference

Conference	Mathematics for Signal and Information Processing
Country/Territory	United States
City	San Diego, CA
Period	2/08/09 → 5/08/09

Scopus Subject Areas

Electronic, Optical and Magnetic Materials
Condensed Matter Physics
Computer Science Applications
Applied Mathematics
Electrical and Electronic Engineering

User-Defined Keywords

Gauss transformation
Lattice
LLL algorithm
Matrix conditioning
Pivoting
Reduced basis
Unimodular matrix

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10.1117/12.834183

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@inproceedings{9019c46ed58b404aa57f00ea23d40aba,

title = "Conditioning properties of the LLL algorithm",

abstract = "Although the LLL algorithm1 was originally developed for lattice basis reduction, the method can also be used2 to reduce the condition number of a matrix. In this paper, we propose a pivoted LLL algorithm that further improves the conditioning. Our experimental results demonstrate that this pivoting scheme works well in practice.",

keywords = "Gauss transformation, Lattice, LLL algorithm, Matrix conditioning, Pivoting, Reduced basis, Unimodular matrix",

author = "LUK, {Franklin T} and Sanzheng Qiao",

year = "2009",

doi = "10.1117/12.834183",

language = "English",

isbn = "9780819477347",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

editor = "Schmalz, {Mark S.}",

booktitle = "Mathematics for Signal and Information Processing",

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TY - GEN

T1 - Conditioning properties of the LLL algorithm

AU - LUK, Franklin T

AU - Qiao, Sanzheng

PY - 2009

Y1 - 2009

N2 - Although the LLL algorithm1 was originally developed for lattice basis reduction, the method can also be used2 to reduce the condition number of a matrix. In this paper, we propose a pivoted LLL algorithm that further improves the conditioning. Our experimental results demonstrate that this pivoting scheme works well in practice.

AB - Although the LLL algorithm1 was originally developed for lattice basis reduction, the method can also be used2 to reduce the condition number of a matrix. In this paper, we propose a pivoted LLL algorithm that further improves the conditioning. Our experimental results demonstrate that this pivoting scheme works well in practice.

KW - Gauss transformation

KW - Lattice

KW - LLL algorithm

KW - Matrix conditioning

KW - Pivoting

KW - Reduced basis

KW - Unimodular matrix

UR - http://www.scopus.com/inward/record.url?scp=70350381150&partnerID=8YFLogxK

U2 - 10.1117/12.834183

DO - 10.1117/12.834183

M3 - Conference proceeding

AN - SCOPUS:70350381150

SN - 9780819477347

T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - Mathematics for Signal and Information Processing

A2 - Schmalz, Mark S.

T2 - Mathematics for Signal and Information Processing

Y2 - 2 August 2009 through 5 August 2009

ER -

Conditioning properties of the LLL algorithm

Abstract

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Scopus Subject Areas

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