On computing multi-dimensional generalized extreme and intermediate eigen subspaces

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

Abstract

In this paper further analysis of the problem of deriving dynamical systems which converge to the minimum and maximum eigenpairs of a symmetric matrix simulaneously have been addressed. Systems that converge to intermediate subspaces are also developed. The derivation of these systems is based on optimizing constrained cost functions over high dimensional unit spheres. Thus necessary and sufficient conditions for optimality of smooth functions over spheres are first derived. In choosing certain cost function, the first order optimality conditions lead to solving a quadratic eigenvalue problem.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages2831-2836
Number of pages6
DOIs
StatePublished - Dec 1 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Keywords

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

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