MA/CSC
580-002: Numerical
Analysis I
Fall Semester, 2008
http://www4.ncsu.edu/~zhilin/TEACHING/MA580
- Time: T TH 4:30-5:45
pm,
Place: HA 335
- Instructor: Dr. Zhilin
Li
Office: HA 333, Tel: 515-3210
- Office hours: 1:30-3:00 pm
E-mail: Click to
E-mai
Goals and Objectives:
This course is designed for students in engineering,
physical
and mathematical sciences. The course covers most of materials in
numerical
linear algebra. We will address issues of algorithm development,
implementation and applicability, the error analysis including effect
of
round off errors, available software packages, and parallel computing
to
some extent. Main topics include: direct and iterative methods
for
solving system of linear equations, least squares solutions,
eigenvalues
problem, singular value decomposition, and non-linear system of
equations.
Textbook:
Numerical Mathematics, A.
Quarteroni, R. Sacco, and F.
Saleri, 2nd Ed. & notes from the instructor
Prerequisites:
A reasonable background in calculus, linear algebra. Some
programming
experiences are helpful, but not essential.
Grading:
Homework (analytic part and computer projects) about
every two weeks: 45%
Class
participation:
5%
(excessive absences will affect the grade linearly)
Midterm & Final
Exam:
Best of 20%+30% or 10% + 40%
Computing:
Matlab will be used for instructions
and is recommended
for homework. However, you can use C, C++, Fortran, or other
computer
language and software packages as well.
Materials:
Introduction: Model problems, round off errors,
norms, condition
numbers.
Direct methods for linear systems, Pivoting, LU, LL'
decomposition.
Iterative methods for linear systems, Jacobi, Gauss-Seidel, SOR,
Spectral
radius, Krylov methods, CG and PCG, GMRES.
Iterative methods for non-linear systems, Newton method and
variations,
Broyden method.
Eigenvalues and other problems in numerical linear algebra,
Eigenvalues
estimation, Power and shifted Power method, Orthogonal transformation,
QR algorithm, Least squares solution, SVD decomposition.
References:
Iterative
Methods
for Linear and Nonlinear Equations, C.T. Kelley, SIAM 1995
Numerical Analysis, Fifth Edition, R. L. Burden and J. D.
Faires,
PWS-Kent Publishing Company, 1993
Matrix Computations, G. Golub and C. F Van Loan, John Hopkins
Calendar:
Jul Aug Sep
S M Tu W Th F S S M Tu W Th F S
H 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
20 21 22 23 21 22 23 24 25 26 27
24 25 26 27 28 29 30 28 29 30
31
Oct Nov Dec
S M Tu W Th F S S M Tu W Th F S S M Tu W Th F S
1 2 3 4 1 1 2 3 4 5 6
5 6 7 V V V 11 2 3 4 5 6 7 8 7 8 9 10 11 12 13
12 13 14 15 16 17 18 9 10 11 12 13 14 15 14 15 F 17 18 19 20
19 20 21 22 23 24 25 16 17 18 19 20 21 22 21 22 23 24 25 26 27
26 27 28 29 30 31 23 24 25 V V V 29
30
H: Holiday, V: Vacation(No class); L: Last day of instruction
M: Midterm Exam; F: 1:00-4:00pm, December 16, in classroom