[ Announcements
| Course Description | Course
Outline | Course
Policy | Homework and Tests | Class
Schedule | Links
]
|
| Announcements
(back to top) |
| |
- 09/30: You can log into BlackBoard to check the grades for
your homework.
- 09/30: Sample questions and sample solutions for Test 1
have been posted.
- 09/20: Homework 2 has been posted.
- 09/09: The Mathlab is now open. You need to go to Mathlab
during its open hours to activate your account on the Linux computers
for doing programming assignments. The schedule for the Mathlab is
posted at http://moya.ic.sunysb.edu/Sinc/Remotes/Math/.
Note
that
after
you
activate
your
account,
you
can
remotely ssh to
compute.mathlab.sunysb.edu at any time using your own or other
computer.
|
| Course
Description (back to top) |
|
Direct methods for solving simultaneous linear equations.
Matrix factorization, conditioning, stability, and efficiency.
Computation of eigenvalues and eigenvectors. Singular value
decomposition.
Prerequisite/Co-requisite: AMS 505, AMS 595
(co-requisite for students without programming experience in C).
Required Textbook
- Numerical Linear Algebra, by Lloyd N. Trefethen and
David Bau, III, SIAM, 1997, ISBN 0-89871-361-7.
Reference Book (not required)
- Matrix Computations, 3rd edition, by Gene H. Golub
and Charles F. Van Loan, John Hopkins University Press, 1996, ISBN
0-8018-5414-8.
|
| Course Outline
(back to top) |
|
Outline
- Matrix
fundamentals, orthogonality, norms, and SVD (2.5
weeks).
- QR
factorization, projectors, Gram-Schmidt algorithm, Householder
triangulation, least squares problems (2 weeks).
- Conditioning
and
stability
(2.5
weeks).
- Solution
of
linear
system
of
equations,
Gaussian
elimination,
pivoting, Cholesky
factorization
(2
weeks).
- Eigenvalue
problems,
Hessenberg
tridiagonalization,
Rayleigh
quotient,
inverse
power
method,
QR
algorithm,
Computing SVD (3 weeks).
- Overview
of
iterative
methods;
Arnoldi/Lanczos
iteration (1.5 week).
- Linear
algebra software (1 week).
|
| Course Policy
(back to top) |
|
Assignments
Homework assignments are due in class typically
one
week
after
they
are
assigned.
You
are
allowed
to discuss course
materials and homework problems in small groups, but limited to
discussion of general ideas only. You must write your solutions
completely independently. Under no circumstances may you copy
solutions from any source, including but not limited to other students
solutions, official solutions distributed in past terms, and solutions
from courses taught at other universities. Violation of these rules may
result in disciplinary actions.
Exams
The exams (including two tests and the final exam) are closed-book,
but
you
are
allowed
to
bring
a
single-sided, one-page, letter-size
cheat sheet, which you must prepare by yourself.
Attendance
All students are expected to attend all the lectures and
exams.
Grading
- Assignments: 30%
- Two tests: 40%
- Final exam: 30%
Note: The lowest score of your homework assignments will be
dropped.
|
| Homework and
Sample Tests
(back to top) |
|
For the computing assignments, you are encouraged to use the
Mathlab SINC Site at Math Tower S-235. You can remotely log onto the
Linux computer compute.mathlab.sunysb.edu
using ssh.
Before you can login, you may need to go to Math Tower S-235 to
activate your account. You may use your own computer if it runs a
UNIX system (such as Linux or Mac OS X), has a C compiler (such as
gcc) and debugger (such as gdb and ddd), and has octave, gnuplot,
and gv (for plotting).
NOTE: The solutions are password
protected. The username is ams526, and the password is fall2009.
Assignments
Sample Tests
|
| Class Schedule
(back to top) |
- Important: All schedules are tentative and are subject
to change.
| Week |
Date |
Topic |
Slides |
Reading |
Notes |
| 1 |
Mon 08/31 |
Course overview; matrix-vector
multiplication |
slides
|
§I.1 |
|
|
Fri 9/4 |
Orthogonal vectors and matrices |
slides
|
§I.2 |
HW1 out |
| 2 |
Mon 9/7 |
No class
(Labor Day observed)
|
|
|
|
|
Fri 9/11 |
Orthogonal matrices; vector norms |
slides |
§I.3 |
|
| 3 |
Mon 9/14 |
Matrix norms |
slides |
§I.3 |
|
|
Fri 9/18 |
Singular value decomposition |
slides
|
§I.4-5 |
HW1 due; HW2 out |
| 4 |
Mon 9/21 |
Projectors, QR factorization |
slides
|
§II.6-7 |
|
|
Fri 9/25 |
Gram-Schmidt orthogonalization |
slides |
§II.8 |
|
| 5 |
Tue 9/29 |
Householder triangularization and
Givens
rotation |
slides |
§II.10
|
|
|
Fri 10/2 |
Least squares problems; review
|
slides |
§II.11 |
HW2 due; HW3 out
|
| 6 |
Mon 10/5 |
Test 1 (covers Part I and Part II
of text book)
|
|
|
|
|
Fri 10/9 |
Floating-point
arithmetic; condition numbers |
slides |
§III.12-13
|
|
| 7 |
Mon 10/12 |
Discussion of Test 1; accuracy and stability |
slides
|
§III.14
|
|
|
Fri 10/16 |
Stability of
algorithms |
slides |
§III.15 |
|
| 8 |
Mon 10/19 |
Stability of Householder QR and back
substitution
|
slides |
§III.16-17 |
Octave
demo trace |
|
Fri 10/23 |
Conditioning of least squares problems
|
slides |
§III.18-19 |
HW3 due; HW4 out |
| 9 |
Mon 10/26 |
Gaussian elimination and LU factorization |
slides |
§IV.20-21 |
|
|
Fri 10/30 |
Stability
of LU |
slides |
§IV.21-22 |
|
| 10 |
Mon 11/2 |
Cholesky factorization; linear
algebra software |
slides |
§IV.23 |
|
|
Fri 11/6 |
Eigenvalue problems; review
|
slides |
§V.24 |
HW4 due; HW5 out |
| 11 |
Mon 11/9 |
Test 2 (covers material up to 11/6) |
|
|
|
|
Fri 11/13 |
Reduction to Hessenberg form |
slides |
§V.25-26 |
|
| 12 |
Mon 11/16 |
Rayleigh
Quotient Iteration |
slides |
§V.27 |
|
|
Fri 11/20 |
QR algorithm without shifts; QR algorithm
with shifts |
slides |
§V.28-29 |
HW5 written-part due; HW6 out
|
| 13 |
Mon 11/23 |
Other eigenvalue algorithms |
|
§V.30 |
|
|
Fri 11/27 |
No class (Thanksgiving break) |
|
|
|
| 14 |
Mon 11/30 |
Computing SVD
|
|
§V.31 |
HW5 programming part due |
|
Fri 12/4 |
Overview of iterative methods; Arnoldi
iterations |
|
§VI.32,33 |
|
| 15 |
Mon 12/7 |
Lanczos iterations |
|
§VI.33,36 |
|
|
Fri 12/11 |
Review
|
|
|
HW6 due
|
| 16 |
Wed 12/16 |
Final exam
(2:15-4:45pm, Melville Library N3074) |
|
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