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:
- Basic iterative methods (Jacobi, Gauss-Seidel, SOR)
-
Kryrov subspace methods (including GMRES, Conjugate Gradient Methods)
- 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:
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.)
Matlab Information:
Please email me if you
have any comments or questions!
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