Repository logo

Infoscience

  • English
  • French
Log In
Logo EPFL, École polytechnique fédérale de Lausanne

Infoscience

  • English
  • French
Log In
  1. Home
  2. Academic and Research Output
  3. Reports, Documentation, and Standards
  4. Low Rank Updates for the Cholesky Decomposition
 
report

Low Rank Updates for the Cholesky Decomposition

Seeger, Matthias  
2004

Usage of the Sherman-Morrison-Woodbury formula to update linear systems after low rank modifications of the system matrix is widespread in machine learning. However, it is well known that this formula can lead to serious instabilities in the presence of roundoff error. If the system matrix is symmetric positive definite, it is almost always possible to use a representation based on the Cholesky decomposition which renders the same results (in exact arithmetic) at the same or less operational cost, but typically is much more numerically stable. In this note, we show how the Cholesky decomposition can be updated to incorporate low rank additions or downdated for low rank subtractions. We also discuss a special case of an indefinite update of rank two. The methods discussed here are well-known in the numerical mathematics literature, and code for most of them can be found in the LINPACK suite.

  • Files
  • Details
  • Metrics
Loading...
Thumbnail Image
Name

cholupdate.pdf

Access type

openaccess

Size

169.86 KB

Format

Adobe PDF

Checksum (MD5)

b17d2e7ce4dcb740bb08c1b83454884b

Logo EPFL, École polytechnique fédérale de Lausanne
  • Contact
  • infoscience@epfl.ch

  • Follow us on Facebook
  • Follow us on Instagram
  • Follow us on LinkedIn
  • Follow us on X
  • Follow us on Youtube
AccessibilityLegal noticePrivacy policyCookie settingsEnd User AgreementGet helpFeedback

Infoscience is a service managed and provided by the Library and IT Services of EPFL. © EPFL, tous droits réservés