An improved LLL algorithm

Franklin T LUK*, Daniel M. Tracy

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

17 Citations (Scopus)


The LLL algorithm has received a lot of attention as an effective numerical tool for preconditioning an integer least squares problem. However, the workings of the algorithm are not well understood. In this paper, we present a new way to look at the LLL reduction, which leads to a new implementation method that performs better than the original LLL scheme.

Original languageEnglish
Pages (from-to)441-452
Number of pages12
JournalLinear Algebra and Its Applications
Issue number2-3
Publication statusPublished - 15 Jan 2008

Scopus Subject Areas

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

User-Defined Keywords

  • Condition number
  • Gauss transformation
  • Integer least squares
  • LLL algorithm
  • Plane reflection
  • QR decomposition
  • Reduced basis
  • Unimodular transformation


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