svd_2006_vt
svd_2006_vt,
"PDE Model Reduction Using the SVD",
a talk I gave on 17 August 2006 at Virginia Tech.
A plain text abstract of the talk is available as
svd_2006_vt.txt.
Please note that the "face" images are used for comparison
and illustration, and come from the work of an entirely
separate research group. That research is described in
Neil Muller, Lourenco Magaia, Ben Herbst,
Singular Value Decomposition, Eigenfaces, and 3D Reconstructions,
SIAM Review,
Volume 46, Number 3, 2004, pages 518-545.
The following files were used:
-
faces_data.png, an image of facial width versus
height data, from Muller, Magaia, and Herbst.
-
faces_eigen.png, the first eight "eigenfaces" extracted
from a dataset, from Muller, Magaia, and Herbst.
-
faces_energies.png, a plot of the 600 singular values
of a facial dataset, from Muller, Magaia, and Herbst.
-
faces_new.png, shows how a face not in the dataset
was approximated using eigenfaces, from Muller, Magaia, and Herbst.
-
faces_three.png, shows the kind of facial images
used in the dataset, and in its testing,
from Muller, Magaia, and Herbst.
-
fsu_logo.pdf, a little FSU logo that appears on
each slide.
-
inout_flow_elements.png, shows the decomposition of
the flow region into elements.
-
inout_flow_energies.png, a plot of the first 16
singular values from the INOUT dataset.
-
inout_flow_hat.png, shows the forcing of the boundary
term by a hat function, when using the reduced model
to solve new problems. (This plot was not used)
-
inout_flow_pod001_dir.eps, the direction field for
the IN/OUT flow, for POD basis vector 1;
-
inout_flow_pod002_dir.eps, the direction field for
the IN/OUT flow, for POD basis vector 2;
-
inout_flow_pod003_dir.eps, the direction field for
the IN/OUT flow, for POD basis vector 3;
-
inout_flow_pod004_dir.eps, the direction field for
the IN/OUT flow, for POD basis vector 4;
-
inout_flow_region.png, shows the flow region.
-
inout_flow_sinusoid_error.png, plots of the error between
an IN/OUT simulation and a CVT approximation using 4, 8 and
16 basis vectors, with a sinusoidal inflow parameter ALPHA;
-
inout_flow_sinusoid.png, shows the forcing of the boundary
term by a sinusoid function, when using the reduced model
to solve new problems.
-
inout_flow_steady_dir.png, the velocity direction field for
the IN/OUT flow field at steady state;
-
inout_flow_step001_dir.png, the velocity direction field for
the IN/OUT flow field at time step 1;
-
inout_flow_step100_dir.png, the velocity direction field for
the IN/OUT flow field at time step 100;
-
sisters.png, several composite photographs made by
Francis Galton;
-
supreme.png, an image of the Supreme Court;
-
svd.png, an illustration from Muller, Magaia, and Herbst
showing the back-rotation, dilation, and roation effects of the SVD.
Last revised on 03 February 2024.