MA/CSC 580-002: Numerical Analysis I
- Time: T TH: 4:30-5:45
PM
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 graduate students majoring
in mathematics. The course covers most of materials in numerical
linear algebra. We will address issues of algorithm
development, implementation, applications and validations, and
available software packages. Main topics include: error
analysis including round-off errors, 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)
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, round off errors & how to reduce them,
vector and matrix norms, condition numbers.
Direct methods for linear systems, pivoting, LU, LL'
decomposition, special matrices.
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.
Eigenvalue problems, 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
Computing Resources:
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: