Lectures: TR 3:05-4:25 pm
Location: Whitaker 1214
Instructor: Edmond Chow
Office Hours: Mondays 3-4 pm in KACB 1312
TA: Long Tran
TA E-mail: firstname.lastname@example.org
TA Office Hours: Thursdays 9-11 am in KACB 1305
Introduction to the state-of-the-art iterative methods for
solving linear and nonlinear systems of equations. This will be
a very practical course, involving Matlab programming and
a student-defined project.
Numerical Linear Algebra (CSE/MATH 6643) or equivalent.
(Note that Numerical Linear Algebra is a completely different course
than Linear Algebra. The latter is an undergraduate math course, sometimes
taught along with differential equations, while
the former is a graduate level course.)
The assignments will require Matlab programming (at least at the level of CS 1371).
- Sparse matrices and review of direct methods
- Basic iterative methods (splitting methods, Jacobi, Gauss-Seidel, SOR)
- Chebyshev iterative method and matrix polynomials
- Krylov subspace methods (conjugate gradient method, GMRES, etc.)
- Projection method framework
- Methods based on biorthogonalization
- Iterative methods for linear least squares
- Multigrid methods
- Domain decomposition
- Nonlinear systems of equations (fixed point methods, Newton, Broyden, Newton-Krylov and other Newton variants for large problems)
- Line search and global convergence
- Contraction mapping and local convergence theory
- Nonlinear least squares (Gauss-Newton, Levenberg-Marquardt)
- Related ideas in optimization
Students will develop facility with iterative methods for the
numerical solution of linear and nonlinear systems, and their analysis.
The students will be able to:
- Given a linear or nonlinear system, choose an
appropriate numerical solution method based on the properties
of the system
- Evaulate a method for its convergence and computational cost,
including parallel computing aspects
- Diagnose convergence problems of iterative solution methods
- Select or design a method or approach for preconditioning
the solution of specific problems
- Use Matlab or other numerical software for solving systems
40% Matlab mini-explorations of concepts covered in class
20% Analytical assignments
30% Student-defined project
10% Class participation
A discussion forum is open on T-square. You are encouraged to use
it to post your questions, to answer other students' questions,
and to discuss all things related to our course material.
Distance Learning Students
All deadlines are on a 1-week later schedule. Also,
you are exempt from the class participation requirement.
- Iterative Methods for Sparse Linear Systems, 2nd edition,
by Yousef Saad, SIAM, 2003.
- Numerical Methods for Unconstrained Optimization and Nonlinear Equations, by J. E. Dennis, Jr. and Robert B. Schabel, SIAM, 1996.
- Matrix Computations, 4th edition,
by Gene Golub and C. F. van Loan, Johns Hopkins, 2013.
You should already have the third book from your course in Numerical
You can order the first two books from SIAM, here
You can get a 30 percent discount if you are a SIAM member.
As a student, you can join SIAM for free, since Georgia Tech is
an Academic Member. Check it out here
These two books are also available electronically from the
Georgia Tech library.