Computing extreme subspaces using Mirsky theorem

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Extreme eigenpairs computation is of considerable interest in signal processing and estimation. Thus problem of simultaneous computation of the smallest and largest eigenvalues and the corresponding eigenvectors of a symmetric matrix is considered. The proposed methods are derived from optimizing cost functions which are chosen to have optimal values at vectors that are linear combinations of extreme eigenvectors of a given matrix. Dynamical systems that converge to extreme eigenvectors are derived from necessary optimality conditions which are given in terms of a gradient of certain cost functions over a Stiefel manifold. Numerical examples are given to examine the convergence.

Original languageEnglish (US)
Title of host publication2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009
Pages2665-2668
Number of pages4
DOIs
StatePublished - 2009
Event2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009 - Taipei, Taiwan, Province of China
Duration: May 24 2009May 27 2009

Publication series

NameProceedings - IEEE International Symposium on Circuits and Systems
ISSN (Print)0271-4310

Other

Other2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009
Country/TerritoryTaiwan, Province of China
CityTaipei
Period5/24/095/27/09

Keywords

  • Eigenvalue spread
  • Gradient dynamical systems; Stiefel manifold
  • Joint PCA-MCA
  • Joint PSA-MSA
  • Oja's rule

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