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
@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",
}