Project:
Computing principal angles for subspaces given by sparse matrices
INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: by appointment
WWW: http://www-math.cudenver.edu/~aknyazev/
Email: aknyazev@math.cudenver.edu
The Background:
A paper
A. V. Knyazev, Merico E. Argentati, An Effective and Robust Algorithm for Finding Principal Angles Between Subspaces Using An
A-Based Scalar Product;
a
revised version submitted to SISC, 2000, describes
algorithms of
computing principal angles between subspaces.
These algorithms are implemented in a MATLAB code
SUBSPACEA.m. The code accurately and relatively efficiently computes
principal angles between subspaces given by
dense matrices of the size n-by-p and n-by-q when
n >> p and n >> q. The code is very inefficient for
subspaces given by
sparse matrices as one of the first steps is
an orthonormalization of the martices, which destroys the sparsity.
The Main Goal:
Changing the code in such a way that no dense matrices
of the size n appear anywhere.
The Project Stages:
1. Obtaining new alternative formulas for
computing principal angles between subspaces, which
do not require using orthogonal basis of subspaces.
Tentative Due Date: November 6.
2. Implementing these formulas in MATLAB.
Tentative Due Date: November 13.
3. Updating the original code
SUBSPACEA.m to include the new algorithm for sparse matrices.
Tentative Due Date: December 10.
The Project Report