CME302 Homework 2
September 30, 2009
T&B 6.1, 6.4, 6.5, 7.1
(1)
Convince yourself that the algorithms 7.1 and 8.1 are indeed equivalent
(here, you do not have to convince us that you’re convinced).
Show that they
are equivalent for a 3x3 matrix of your choice.
(2)
Load ’
cameraman.tif
’ and view it in
Matlab
as follows:
A = double(imread(’cameraman.tif’));
imagesc(A); colormap(gray); axis image;
(a)
Describe how to construct the rank
k
approximation
B
k
to
A
. Show us your
code. (You can do this in two lines of
Matlab
code.)
Feel free to download
mon1.m
from the Materials section of Coursework to
compare your solution with the one displayed by
mon1.m
.
(The code to form
the approximation is of course in
mon1.m
, but don’t look at it unless you are
desperate: that would take away the fun.)
(b)
Let us define the relative error to be
e
=
bardbl
A
−
B
k
bardbl
F
bardbl
A
bardbl
F
.
What rank does
B
k
have to have to give a relative error of 10%? 1%? (Do this
in
Matlab
.)
(3)
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 Fall '09
 Numerical Analysis, Surround sound, Singular value decomposition, singular values, Bk

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