Symmetry and the Karhunen-Loève analysis

Nejib Smaoui, Hans Armbruster

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


The Karhunen-Loève (K-L) analysis is widely used to generate low-dimensional dynamical systems, which have the same low-dimensional attractors as some large-scale simulations of PDEs. If the PDE is symmetric with respect to a symmetry group G, the dynamical system has to be equivariant under G to capture the full phase space. It is shown that symmetrizing the K-L eigenmodes instead of symmetrizing the data leads to considerable computational savings if the K-L analysis is done in the snapshot method. The feasibility of the approach is demonstrated with an analysis of Kolmogorov flow.

Original languageEnglish (US)
Pages (from-to)1526-1532
Number of pages7
JournalSIAM Journal on Scientific Computing
Issue number5
StatePublished - Sep 1997


  • Karhunen-Loève analysis
  • Optimal eigenfunctions
  • Symmetry

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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