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:
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.
Matlab Information:
Please email me
if you have any comments or questions!
Go back
to MAT 229A home page