Numerical properties of the LLL algorithm

Franklin T Luk, Sanzheng Qiao*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

3 Citations (Scopus)


The LLL algorithm is widely used to solve the integer least squares problems that arise in many engieering applications. As most practitioners did not understand how the LLL algorithm works, they avoided the issue by referring to the method as an integer Gram Schmidt approach (without explaining what they mean by this term). Luk and Tracy1 were first to describe the behavior of the LLL algorithm, and they presented a new numerical implementation that should be more robust than the original LLL scheme. In this paper, we compare the numerical properties of the two different LLL implementations.

Original languageEnglish
Title of host publicationAdvanced Signal Processing Algorithms, Architectures, and Implementations XVII
Publication statusPublished - 2007
EventAdvanced Signal Processing Algorithms, Architectures, and Implementations XVII - San Diego, CA, United States
Duration: 26 Aug 200727 Aug 2007

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


ConferenceAdvanced Signal Processing Algorithms, Architectures, and Implementations XVII
Country/TerritoryUnited States
CitySan Diego, CA

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
  • LLL algorithm
  • Numerical overflow and underflow
  • Plane reflection
  • QR decomposition
  • Reduced basis
  • Unimodular transformation


Dive into the research topics of 'Numerical properties of the LLL algorithm'. Together they form a unique fingerprint.

Cite this