Lexing Ying

M393D: Iterative Linear Algebra

Course information:

Instructor: Lexing Ying, lexing@math.utexas.edu, 471-3149, RLM 10.164
Lecture: TTh 12:30-2pm, RLM 11.176
Office hour: TTh 2-3pm.
Webpage: http://www.math.utexas.edu/users/lexing/courses/Fall2007_M393D/index.html

Textbook:

We will mostly follow

Iterative methods for sparse linear systems by Yousef Saad (2nd edition). The first edition can be found at the author's website.

Other useful references include:

Matrix computation by Golub and Van Loan
A first course in the numerical analysis of differential equations by Iserles
A multigrid tutorial by Briggs et al.
Domain decomposition: parallel multilevel methods for elliptic partial differential equations by Smith et al.
Convex optimization by Boyd and Vandenberghe (electronic copy available from the book website)
Numerical optimization by Nocedal and Wright (electronic copy available from library website)

Prerequisite and degree relevance:

Linear algebra. Some knowlege about programming in Matlab, C or Fortran.

Course description:

This course covers:

Classical iterative methods
Krylov subspace iterative methods
Preconditioners
Multigrid
Domain decomposition
Basic convex optimization
Fast algorithms for structured matrices.

Week	Tue	Thu
1 Aug 27	No class	Introduction. Basic iterative methods (Chap4)
2 Sep 3	Basic iterative methods. (Chap 4)	Projection methods (Chap 5)
3 Sep 10	Projection methods. Arnoldi (Chap 6)	Arnoldi (Chap 6)
4 Sep 17	GMRES (Chap 6)	Lanczos (Chap 6)
5 Sep 24	Travel	CG (Chap 6)
6 Oct 1	CG (Chap 6)	Convergence Analysis (Chap 6)
7 Oct 8	Biorthogonalization. BCG et al.	Preconditioning. ILU(k)
8 Oct 15	Approximate inverse preconditioners	Multigrid
9 Oct 22	Multigrid. Algebraic multigrid	Algebraic multigrid
10 Oct 29	Domain decomposition	Domain decomposition
11 Nov 5	Domain decomposition	Convex optimization
12 Nov 12	Convex optimization	Convex optimization
13 Nov 19	FFT, nonuniform FFT	Thanksgiving
14 Nov 26	Fast multipole method	Fast multipole method
15 Dec 3	Adjoint method	Johnson Lindenstrauss Lemma

Grading:

Mostly based on attendance and homework.

Homeworks:

HW01
HW02

Notes:

Disabilities:

The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Policy on scholastic dishonesty:

Students who violate university rules on scholastic dishonesty are subject to disciplinary penalties, including the possibility of failing in the course and/or dismissal from the University. Since such dishonesty harms the individual, all students, and the integrity of the University, policies on scholastic dishonesty will be strictly enforced. For further infomation, please visit the Student Judicial Services web site at http://deanofstudents.utexas.edu/.