Paper ID sheet UCL-INMA-2007.032

Title

Continuous-time subspace flows related to the symmetric eigenvalue problem

Authors

P.-A. Absil, R. Sepulchre, R. Mahony

Abstract

The classes of continuous-time flows on $\Re^{n\times p}$ that induce the same flow on the set of $p$-dimensional subspaces of $\Re^n$ are described. The power flow is briefly reviewed in this framework, and a subspace generalization of the Rayleigh quotient flow [Linear Algebra Appl. 368C, 2003, pp.~343--357] is proposed and analyzed. This new flow displays a property akin to deflation in finite time.

Key words

Matrix flows; subspace flows; power flow; Grassmann Rayleigh quotient flow; principal component analysis; invariant subspace; finite-time deflation

Status

Pacific Journal of Optimization (PJO), Volume 4, Number 2, 179--194, May 2008

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• Publisher's version: http://www.yokohamapublishers.jp/online2/pjov4-1.html
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BibTeX entry

@ARTICLE{AbsSepMah2008,
  author = "Absil, P.-A. and Sepulchre, R. and Mahony, R.",
  title = "Continuous-time subspace flows related to the symmetric eigenproblem",
  journal = "Pac. J. Optim.",
  year = 2008,
  volume = 4,
  number = 2,
  pages = "179--194",
}