%brief description of all the m-files in UTV Tools
(Version 1.0 22-June-99 for Matlab 5.2)

% Demonstration M-files
hulvdemo.m - high-rank ULV algorithms hulv.m and hulv_a.m
hurvdemo.m - high-rank URV algorithms hurv.m and hurv_a.m
lulvdemo.m - low-rank ULV algorithms lulv.m and lulv_a.m
lurvdemo.m - low-rank URV algorithms lurv.m and lurv_a.m
rrqrdemo.m - high- and low-rank RRQR algorithms hrrqr.m and lrrqr.m
ullvdemo.m - high-rank ULLV algorithm ullv.m, and the up- and downdating
             algorithms ullv_up_a.m and ullv_dw_a.m
wulvdemo.m - ULV up- and downdating algorithms, implemented in ulv_win.m
wurvdemo.m - URV up- and downdating algorithms, implemented in urv_win.m

% UTV-Based Solvers
tulv.m - Solves a numerically rank-deficient least squares problem
         using the rank-revealing ULV decomposition.
turv.m - Solves a numerically rank-deficient least squares problem
         using the rank-revealing URV decomposition.

% High-Rank UTV Algorithms
hulv.m   - Stewart's rank-revealing ULV algorithm.
hulv_a.m - The alternative rank-revealing ULV algorithm.
hurv.m   - Stewart's rank-revealing URV algorithm.
hurv_a.m - The alternative rank-revealing URV algorithm.

% Low-Rank UTV Algorithms
lulv.m   - Warm-started rank-revealing ULV algorithm.
lurv.m   - Warm-started rank-revealing URV algorithm.
lulv_a.m - Cold-started rank-revealing ULV algorithm.
lurv_a.m - Cold-started rank-revealing URV algorithm.

% Block QR Refinement
ulv_qrit.m - Refinement of L in the ULV decomposition.
urv_qrit.m - Refinement of R in the URV decomposition.

% UTV Up- and Downdating
ulv_dw.m  - Downdate the rank-revealing ULV decomposition.
ulv_up.m  - Update the rank-revealing ULV decomposition.
ulv_win.m - Sliding window modification of the rank-revealing
            ULV decomposition
urv_dw.m  - Downdate the rank-revealing URV decomposition.
urv_up.m  - Update the rank-revealing URV decomposition.
urv_win.m - Sliding window modification of the rank-revealing
            URV decomposition.

% ULLV Algorithms
ullv.m      - Compute a high-rank revealing ULLV decomposition.
ullv_dw_a.m - Downdate A in the rank-revealing ULLV decomposition.
ullv_dw_b.m - Downdate B in the rank-revealing ULLV decomposition.
ullv_up_a.m - Update A in the rank-revealing ULLV decomposition.
ullv_up_b.m - Update B in the rank-revealing ULLV decomposition.

% RRQR Algorithms.
hrrqr.m - Chan/Foster high-rank RRQR algorithm.
lrrqr.m - Chan-Hansen low-rank RRQR algorithm.
trrqr.m - Solves a numerically rank-deficient least squares problem
          using the RRQR decomposition.

% Misc. Tools.
app_giv.m   - Apply a Givens rotation (from the left or right).
app_hous.m  - Apply a Householder reflection (from the left or right).
ccvl.m      - Estimation of the smallest singular value via Cline-Conn-Van Loan algorithm.
gen_giv.m   - Determine a 2-by-2 Givens rotation matrix.
gen_hous.m  - Determine a Householder reflection matrix.
inviter.m   - Estimation of the smallest singular value via inverse iteration.
lanczos.m   - Estimation of the largest singular value via Lanczos bidiagonalization.
mgsr.m      - Modified Gram-Schmidt with re-orthogonalization (expansion step)
powiter.m   - Estimation of the largest singular value via the power method.
ullv_csne.m - Corrected semi-normal equations expansion step (ULLV).
ullv_rdef.m - Deflate one row of LA in the ULLV decomposition.
ullv_ref.m  - Refine one row of LA in the ULLV decomposition.
ulv_cdef.m  - Deflate one column of L in the ULV decomposition.
ulv_csne.m  - Corrected semi-normal equations expansion step (ULV).
ulv_rdef.m  - Deflate one row of L in the ULV decomposition.
ulv_ref.m   - Refine one row of L in the ULV decomposition.
urv_cdef.m  - Deflate one column of R in the URV decomposition.
urv_csne.m  - Corrected semi-normal equations expansion step (URV).
urv_rdef.m  - Deflate one row of R in the URV decomposition.
urv_ref.m   - Refine one column of R in the URV decomposition.

% <Revision>
% Ricardo D. Fierro, California State University San Marcos
% Per Christian Hansen, IMM, Technical University of Denmark
% Peter S.K. Hansen, IMM, Technical University of Denmark

% (UTV Tools) Last revised: June 22, 1999