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MAT 229A Syllabus Page (Winter, 2002)
Course: MAT 229A CRN: 61378 Title: Numerical Methods in Linear Algebra Class: TTh 12:10pm-1:30pm, Wellman 129
Instructor: Naoki Saito Office: 675 Kerr Phone: 754-2121 Email:saito@math.ucdavis.edu Office Hours: TTh 2:00pm-3:00pm or by appointment via email
Course Objective:
Numerical linear algebra is a subject of tremendous importance for scientific
and engineering applications. The course objectives include:
To learn and understand important concepts and algorithms of numerical
linear algebra so that one will be able to choose appropriate algorithms
for their own problems and will be able to use the packages not as a
complete black box.
To have an experience of applying such algorithms to simple yet practical
problems in science and engineering. I will use examples ranging from
image processing to geophysical inverse problems.
Topics:
The following topics will be covered:
Singular Value Decomposition (SVD)
Projections, QR Factorization, and Least Squares Problems
Conditioning, Stability, and Ill-Posed Problems
Applications of the above to Image Processing, Statistics, and
Inverse Problems
Text:
We use the following text with some supplemental papers and handouts.
Required: L.N.Trefethen and D.Bau, III, Numerical Linear Algebra,
SIAM, 1997.
Optional: J.Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
Optional: R. A. Horn and C. R. Johnson, "Matrix Analysis," Cambridge
University Press, 1985.
Prerequisite:
Strong motivation to solve your problems in your own field.
Basic understanding of linear algebra, such as MAT 22A, 167, or equivalent.
Some familiarity with numerical experiments on computer, such as MAT
128AB or equivalent (not necessarily to have extensive experience)
Some experience in Matlab is preferable, but not required.
Class Web Page:
I will maintain the Web pages for this course (one of which you are looking
at now). All homework assignments and important announcements will be posted
on these pages. Please check these pages regularly.
You can access the 229A home page at
https://www.math.ucdavis.edu/~saito/courses/229A/
from which you can access to
this syllabus page
and the
homework page.
Class Mailing List:
The MAT 229A Mailing List was created.
You can submit your public comments, suggestions, and questions on HW,
and/or some useful information related to the class to this mailing list.
Once you send your email to this list, everyone will receive it.
So, please use this wisely and politely. Its name is:
mat229a-w02@ucdavis.edu.
Grading Scheme:
50% Homework
50% Final Report
Homework:
I will assign homework including both analytical and programming exercises
every other Thursday. Its due date is the following due date. In principle,
I will collect the homework at the beginning of the lecture on that due date.
LATE HOMEWORK WILL NOT BE ACCEPTED. Please use the word processing software
if possible, but it is not mandatory. If you decide to hand write, please
write your solutions nicely so that I can read them.
A subset of these problems will be graded.
Working in a small group (2 to 3 students) are allowed.
Click here
to go to homework page.
Final Report:
The other half of your grade will be determined by your final report. Here,
you need to write a report on one of the following topics:
Describe how some of the algorithms you learned in this course will
be used in your research; or
Find out an interesting problem (e.g., problems in applied areas including
but not limited to: biology, electrical engineering, geophysics, statistics,
etc.) whose solution requires the least squares method. Then solve that
problem numerically using: 1) SVD; 2) QR; 3) Normal Equations. Finally, analyze
and compare these solutions, their stabilities, and measure their computational
cost on your computer to check whether they agree with the theoretical predictions.
Another Matlab primer is also available as a
Postscript file
and a PDF
file
. The chapter of sparse matrices of the Matlab manual is available
as a Postscript
file
and a PDF
file
. Please take a look at them.