# The continuous-time Rayleigh quotient flow on the sphere

- AUTHORS: R. Mahony, P.-A. Absil.
- ABSTRACT:

A continuous-time differential equation analogous to the Rayleigh
Quotient Iteration for a symmetric matrix $A$ is studied. The set
of all continuous solutions, termed the Rayleigh quotient flow,
is shown to be a scaled version of the Newton flow for Rayleigh
quotient cost functional. The scaling factor ensures that the
rate of variation of the Rayleigh quotient is constant and
positive along solutions. This interpretation leads to a precise
phase portrait for Rayleigh quotient flow. In particular, it is
shown that complete solutions of the Rayleigh quotient flow visits
the eigenvectors of $A$ in ascending order.
- STATUS: published in Linear Algebra and its Applications, Volume 368,
15 July 2003, Pages 343-357.
- DATE OF ENTRY: March 2001.

[Home]