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Department of Mathematics
Fall 2002
APMA 920 - Numerical Linear Algebra
Maintained by Benjamin Ong
I guess I couldn't find the motivation to update this
webpage on a regular basis. sigh. I did however put
my writeup and codes in my
papers section which you're
more than welcome to download and read. I looked at
SPARSE LU orderings.
Happy Halloween... Here'a plot that could help
you in Lecture 21.2
here's a code to test the stability of an SVD
decomposition. (
lec16_q2.m
)
Exercise 12.2 (
lec12_2.m
) wants us to show that polynomial interpolation
is an unstable algorithm as is shown through the following picture
and gets us to plot the Lebesgue constants for equispaced
interpolation
The following script files are for exercise 10.2,
(and are needed also for exercise 11.3).
house.m
computes an implicit representation of a full QR
factorization using Householder reflections.
The columns of W are vectors defining sucessive
Householder reflections
formq.m
takes the matrix W produced by house.m and generates
the corresponding orthogonal matrix q.
Here is my matlab driver file (
lec11_ex3.m )
that shows how roundoff error is present in
unstable QR algorithms. You will also need
the following helper functions:
backsubs.m
Code for solving Ux=b where U is upper triangular
forwardsubs.m
Code for solving Lx = b where L is lower triangular
formqb.m
Implicit calculation of a product Q*B using
W from house.m .
I've decided to make my codes for the course available
on this webpage. I don't promise I'll update it regularly,
but you're welcome to harass me about it. Here's a plot from
HW 3 generated from
a3.m showing the Legendre polynomials
and the rate of convergence of the approximations.
Here are some other codes that I've done from Lecture 9.
clgs.m
QR factorization via Classical Gram-Schmidt
mgs.m
QR factorization via modified Gram-Schmidt
lec9_exp2.m
Lecture 9 experiment 2, code shows how singular
values of a matrix are affected by roundoff error.
