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MAT 229B Syllabus Page (Winter, 2000)
Course: MAT 229B CRN: 91331 Title: Numerical Methods in Linear Algebra Class: MWF 12:10pm-1:00pm, Wellman 127
Instructor: Naoki Saito Office: 675 Kerr Phone: 754-2121 Email:saito@math.ucdavis.edu Office Hours: MW 1:15pm-2:15pm or by appointment via email
Course Objective:
To learn a certain class of numerical linear algebra algorithms (in particular,
iterative methods and sparse matrix algorithms) using some model problems such
as discrete inverse problem or Poisson equations including:
We also choose a few topics from
FFT-based methods, wavelet-based methods, and multigrid methods
If time allows, we also discuss the total-least squares method and other inverse problems.
Text:
We use the following text with many 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: G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd Ed.,
Johns Hopkins Univ. Press, 1996.
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, and MAT 229A is
not a prerequisite of this course)
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 229B home page at https://www.math.ucdavis.edu/~saito/courses/229B/ from which you can access to this
syllabus page and the homework page.
Grading Scheme:
50% Homework
50% Final Report
Homework:
I will assign homework including both analytical and programming exercises
every other Friday. 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. A subset of these
problems will be graded.
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:
Description on how the algorithms you learned in this course will be used
in your thesis research with brief description of your thesis objectives and
problem setting; or
Quantitative comparison of the several methods learned
in this class for 1) solving the Poisson equation with given boundary
conditions; or 2) reconstructing images from the given projections.
(These boundary conditions and the projection data will be specified later.)