|
Home
Research
Publications
MA614
MA626
Archived Lectures:
MA515
MA526
MA626
MA614
MA238
MA502
MA201
MA506
DMS
UAH
|
|
UAH, Spring Semester
| |
MA 614 |
| Faculty: |
Prof.
S.S. Ravindran |
| Lecture Room: |
Madison Hall 330 |
| Lecture Time: |
MW 2:20 p.m - 3:40 p.m. |
| Office Hours: |
TRF 3:00 - 5:00 p.m. |
MA614:
Numerical Linear Algebra
|
Fundamentals of Matrix Computations,
by David Watkins ;
John Wiley and Sons, 2nd Edition, 2002.
Errata list (pdf).
Additional References:
Matrix Computations,
by Gene Golub and Charles Van Loan ;
The Johns Hopkins Press.
Applied Numerical Linear Algebra,
by James W. Demmel ;
SIAM.
Numerical Linear Algebra by L.N.Trefethen and D.Bau, SIAM, 1997.
Applied Numerical Linear Algebra by W.W. Hager.
G. W. Stewart: Introduction to Matrix Computations, Academic Press, 1973.
D.S. Bernstein, Matrix mathematics, Princeton University Press,
Princeton, NJ, 2005. ISBN: 0-691-11802-7
A. Bjorck, Numerical methods for least squares problems, SIAM,
Philadelphia, PA, 1996. ISBN: 0-89871-360-9
This is a first course in numerical linear algebra, i.e., the use
of scientific computing to solve problems that arise from linear algebra,
such as linear systems, least squares problems, and the algebraic
eigenvalue problem.
- Silultaneous Solution of Linear Systems
- Gaussian Elimination and its Variants :
Cholesky Decomposition, Gaussian Elimination with partial pivoting, LU decomposition.
- Sensitivity of Linear Systems :
Norms, Condition numbers, A Posteriori Error Analysis, Bacward Stability,
Propagation of Roundoff Errors, Backward Error Analysis.
- Iterative Methods :
Jacobi, Gauss-Seidel and SOR iterative methods, Red-Black and multi color
iterative methods, Descent
Methods, Preconditioners, Conjugate Gradient Method. Convergence of iterative methods
- Least Squares Problems:
-
Discrete Least Squares Problem (Over determined, under-determined and rank deficient
problems), Orthogonal Matrices, Rotators, and Reflectors,
Solution of the Least Squares Problem, The Gram-Schmidt Process
- The Sigular Value Decomposition :
Some basic Applications of Sigular Values, The SVD and the Least Squares
Problems
- Eigenvalues and Eigenvectors :
- Methods for Symmetric Matrices:
Reduction to
Tridiagonal Forms, Jacobi algorithm, Divide and Conquer algorithm,
Spectrum slicing algorithm.
- Methods for General Matrices:
The Power Method, Raleigh quitient and inverse iteration, Reduction to Hessenberg Form and
QR algorithm with and without shifts
Linear algebra (MA544 or 508), numerical analysis (415 or 515) and
computer programming proficiency.
At least one of the following programming languages:
MATLAB, Fortran, C.
Hourly examinations
There will be one 1:20 minute in-class midterm examination during the semester.
This is scheduled for March 14.
Final examination
There will be a comprehensive final examination on
April 30 from 3:00-- 5:30pm.
Make-ups
If you miss a test due to a documented
illness, family emergency or other extreme circumstance, the weight of
your remaining grades will be adjusted to compensate provided I receive
a written excuse within a reasonable amount of time
after the missed test.
Calculators
No programmable or Graphic calculators are allowed in the
tests. Only basic calculators are allowed.
If the calculator costs more than $15, you are buying the wrong calculator.
Assignments
I will give assignments nearly every week,
to be turned in for grading. This average will count 35% of
your grade. Your assignment must be neatly written with appropriate
discussions and stapled. Do not fold it or include it in envelope.
Practice Assignments
Practice homework will be written on blackboard at the end of each section.
These are for practice only and will not be collected or graded.
If you have questions about them you may work with
your classmates, ask me for assistance, and/or ask some questions
during class. (We will not have time to answer all the
questions in class.)
Course grading
Each student's grade will be based on the individual grades
from exams and assignments. The approximate percentage weights
are as follows:
Grade Weights
| Item |
Approx.
Weight |
| Mid-term Exam |
30% |
| Final Exam |
35% |
| Assignments |
35% |
| Total |
100% |
Grading Scale
| A |
90.0 - 100% |
| B |
80.0 - 89% |
| C |
70.0 - 79% |
| D |
60.0 - 69% |
| F |
Below 60.0% |
| Week |
Sections |
Comments |
| 1 |
Review |
..... |
| 2 |
1.8 |
..... |
| 3 |
2.1,2.2 |
..... |
| 4 |
2.3 |
..... |
| 5 |
2.4,3.1 |
..... |
| 6 |
3.2 |
...... |
| 7 |
3.3,3.4 |
..... |
| 8 |
4.1,4.2 |
..... |
| 9 |
4.3,5.3 |
..... |
| 10 |
5.6 |
Midterm Exam on 03/14 in class |
| 11 |
..... |
No Classes - Spring Break
|
| 12 |
6.5,7.2 |
..... |
| 13 |
7.3,7.4 |
..... |
| 14 |
7.5,7.6 |
........ |
| 15 |
7.7,7.8 |
........ |
| 15 |
Review |
Final Exam: 3:00--5:30pm, April 30
|
Note: This is an approximate syllabus only and because of
differences in weekly schedules, some variations are to be
expected.
| Section |
Exercises |
| 1.8 |
4,7,16,17
|
| 2.1 |
15,16,17,23,28,30,31,32
|
| 2.2 |
6,13,14,21,23,29,30
|
| 2.3 |
12
|
| 2.4 |
2,3,4,5
|
| 3.1 |
5,6,7,8,9
|
| 3.2 |
3,4,5,7,8,9,12,14,16,17,19,21,25,27,29,33,38,39,41,48,49
|
| 3.3 |
4,7,9,10,13,15
|
| 3.4 |
4,5,6,9,10,22,24,26,29,30,31
|
| 4.1 |
6,15,16
|
| 4.2 |
3,8,10,12,19,20
|
| 4.3 |
4,8,9,10,11
|
| 5.3 |
6,7,8,9,10,11,12,13,14,15,16.
|
| 5.6 |
2,4,6,8,10,12,14,15,20,22
|
| 7.2 |
4,7,12,18,24
|
| 7.3 |
3,10,11,12
|
| 7.4 |
4,8,12,18
|
A free PDF viewer is available for most computer systems from
clicking on the the icon shown below.
- Old Midterm
- Old Final 2007
- Old Final 2003
Instructions for Computer Write-ups:
Click here for a sample
computer write-up
FINAL EXAM
3:00-5:30 pm, April 30
Class attendance, preparation, and participation are required. Learning
this course is not a spectator sport. Students having difficulties
should seek assistance from the instructor. Students are encouraged to
work together on problems that will not be graded. Students are expected
to be honest and ethical at all times.
Students with disabilities needing academic accommodations should
1) register with and provide
documentation to the Student Development Services Office,
and 2) bring a letter to the instructor from SDSO indicating you need academic
accommodations. This should be done within the first week of class.
A Practical Introduction to Matlab
|
