MA/CSC 580-001: Numerical
Analysis
Fall Semester, 2019
- Time: MWF: 9:35-10:25
AM
Place: SAS 1218
- Instructor: Dr. Zhilin
Li
Office: SAS 3148, Tel: 919-515-3210
- E-mail: zhilin@ncsu.edu
Office hours:
Mondays:
2:10-2:50pm; Wednesday: 10:30-11:15am, or by appointment
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: e-Books at NCSU:
Prerequisites:
A reasonable background in calculus, linear algebra.
Some programming experiences are helpful, but not essential.
Grading:
Homework (analytic part and computer
projects): 65%; A Take-Home Test: 35%.
Class
participation: + or -
3% (excessive absences will affect the grade
linearly)
Week 1 (8/22),
Week 2 (8/29),
Week 3 (9/5), Week 4 (9/12), Week 5 (9/19), Week
6 (9/26), Week 7 (10/5), Week 8
(10/3), Week 9 (10/10),
Week 10 (10/17), Week 11 (10/24), Week
12 (10/31), Week 13
(11/7), Week 14
(11/14), Week 15
(11/21), Week 16 (11/28), Week
17 (12/5)
Computing:
Matlab will be used for instructions
and is recommended for homework. However, you can use
Python, C, C++, Fortran, or other computer language and software
packages as well.
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.
Other References:
Iterative
Methods
for
Linear and Nonlinear Equations, C.T. Kelley, SIAM
Numerical Analysis, Fifth Edition, R. L. Burden and J.
D. Faires, PWS-Kent Publishing Company, (under-graduate
textbook)
Numerical
Matrix Analysis, I. Ipsen, SIAM.
Matrix Computations, G. Golub and C. F Van Loan, John Hopkins
A
link to significant digits.
Tacoma
Bridge Collapse: 1940 Explanation: 1. Oscillation of bridge caused by the wind
frequency being too close to the natural frequency of the bridge 2. Natural frequency of thebridge is the eigenvalue of the smallest magnitude
(based on a system that modeled the bridge)
Computing Resources:
Two_Point_SOR
Matlab Codes:
Calendar:
July August September
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
1 2 3 1 H 3 4 5 6 7
7 8 9 10 11 12 13 4 5 6 7 8 9 10 8 9 10 11 12 13 14
14 15 16 17 18 19 20 11 12 13 14 15 16 17 15 16 17 18 19 20 21
21 22 23 24 25 26 27 18 19 20 F B 23 24 22 23 24 25 26 27 28
28 29 30 31 25 26 27 28 29 30 31 29 30
October November December
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
1 2 3 4 5 1 2 1 2 3 4 5 L 7
6 7 8 9 V V 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14
13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21
20 21 22 23 24 25 26 17 18 19 20 21 22 23
27 28 29 30 31 24 25 26 H H H 30
H: Holiday, V: Vacation(No class); L:
Last day of instruction
M: Midterm Exam; F: