UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: NOON (Refreshments served at 11:45 am)

DATE: April 30, 2001

Title:
Principal Angles between Subspaces in an A-Based
Scalar Product: Algorithms and Perturbation Estimates


Speaker:
   Rico Argentati, University of Colorado Denver



Abstract:

Computation of principal angles between subspaces is important in 
many applications, e.g., in statistics and information retrieval. 
In statistics, the angles are  closely related to measures of dependency 
and covariance of random variables. When applied to column-spaces of
matrices, the principal angles describe canonical correlations of a 
matrix pair. Also, there are practical applications involving analysis 
of algorithms, convergence rates, when orthogonal projections commute, etc.

All current popular software codes for canonical correlations compute 
only the cosine of principal angles, making it impossible to find small 
angles accurately due to round-off errors.  In this talk 
I will review a combination of sine and cosine based algorithms that 
provide accurate results for all angles. This method generalizes 
the computation of principal angles in an A-based scalar product to 
symmetric and positive definite matrices. An overview of interesting 
properties of principal angles will be discussed, as well as perturbation 
theorems for absolute errors for sine and cosine of principal angles 
with improved constants. Numerical examples and applications are presented.

This talk is based on a recent paper by A. V. Knyazev and M. E. Argentati, 
Principal Angles between Subspaces in an A-Based Scalar Product: 
``Algorithms and Perturbation Estimates'' that has been
submitted to SISC, and a technical report UCD-CCM 163, 2000, at the
Center for Computational Mathematics, University of Colorado.