The continuous-time Rayleigh quotient flow on the Grassmann manifold
- AUTHORS: P.-A. Absil, R. Mahony, R. Sepulchre.
An extension of the Rayleigh quotient iteration (RQI) to the Grassmann manifold
has been recently proposed for computing a $p$-dimensional eigenspace of a
symmetric matrix $A$. Here we analyze a continuous-time flow analogous to this
Grassmannian RQI. This flow achieves deflation in finite time, i.e.\ it
converges in finite time to a subspace that includes an eigenvector of $A$.
- STATUS: Proceedings of the Fifteenth International Symposium on
Mathematical Theory of Networks and Systems (MTNS 2002), University of
Notre Dame, August 12-16, 2002.
- DATE OF ENTRY: March 2001.