A pivoted LLL algorithm

Franklin T Luk; Sanzheng Qiao

doi:10.1016/j.laa.2010.04.003

A pivoted LLL algorithm

Franklin T Luk, Sanzheng Qiao

Research output: Contribution to journal › Journal article › peer-review

2 Citations (Scopus)

Abstract

Luk and Tracy (2008) [7] developed a matrix interpretation of the LLL algorithm. Building on their work [7], we propose to add pivoting to the algorithm. We prove that our new algorithm always terminates, and we construct a class of ill-conditioned reduced matrices to illustrate the advantages of pivoting.

Original language	English
Pages (from-to)	2296-2307
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	434
Issue number	11
DOIs	https://doi.org/10.1016/j.laa.2010.04.003
Publication status	Published - 1 Jun 2011

Scopus Subject Areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

User-Defined Keywords

Conditioning
Lattice basis reduction
LLL algorithm
Pivoting

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10.1016/j.laa.2010.04.003

Cite this

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title = "A pivoted LLL algorithm",

abstract = "Luk and Tracy (2008) [7] developed a matrix interpretation of the LLL algorithm. Building on their work [7], we propose to add pivoting to the algorithm. We prove that our new algorithm always terminates, and we construct a class of ill-conditioned reduced matrices to illustrate the advantages of pivoting.",

keywords = "Conditioning, Lattice basis reduction, LLL algorithm, Pivoting",

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

note = "Funding Information: Sanzheng Qiao is partially supported by Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University) and NSER∗ Correspondingauthor.CofCanada. E-mail address: [email protected] (F.T. Luk).",

year = "2011",

month = jun,

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doi = "10.1016/j.laa.2010.04.003",

language = "English",

volume = "434",

pages = "2296--2307",

journal = "Linear Algebra and Its Applications",

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TY - JOUR

T1 - A pivoted LLL algorithm

AU - Luk, Franklin T

AU - Qiao, Sanzheng

N1 - Funding Information: Sanzheng Qiao is partially supported by Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University) and NSER∗ Correspondingauthor.CofCanada. E-mail address: [email protected] (F.T. Luk).

PY - 2011/6/1

Y1 - 2011/6/1

N2 - Luk and Tracy (2008) [7] developed a matrix interpretation of the LLL algorithm. Building on their work [7], we propose to add pivoting to the algorithm. We prove that our new algorithm always terminates, and we construct a class of ill-conditioned reduced matrices to illustrate the advantages of pivoting.

AB - Luk and Tracy (2008) [7] developed a matrix interpretation of the LLL algorithm. Building on their work [7], we propose to add pivoting to the algorithm. We prove that our new algorithm always terminates, and we construct a class of ill-conditioned reduced matrices to illustrate the advantages of pivoting.

KW - Conditioning

KW - Lattice basis reduction

KW - LLL algorithm

KW - Pivoting

UR - http://www.scopus.com/inward/record.url?scp=79952625584&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2010.04.003

DO - 10.1016/j.laa.2010.04.003

M3 - Journal article

AN - SCOPUS:79952625584

SN - 0024-3795

VL - 434

SP - 2296

EP - 2307

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 11

ER -

A pivoted LLL algorithm

Abstract

Scopus Subject Areas

User-Defined Keywords

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