MATH6800/CSCI6800 Computational Linear Algebra

MR 10.0-11.50 Carnegie 112 Fall 2000

Course Outline

I intend to follow this outline fairly closely.

1.

Introduction.  

2.

Gaussian elimination. Including backward error analysis, Cholesky factorization, sparse matrices, ...  

3.

Least squares problems. Including QR factorization, singular value decomposition, orthogonal matrices ...  

4.

Eigenvalue problems. Including the nonsymmetric and symmetric cases, the use of the SVD, ...  

5.

Iterative methods. Including the conjugate gradient method, the fast Fourier transform, the Lanczos algorithm ...  

Homework:

Approximately every two weeks. You should learn a fair amount from the homeworks. Therefore, try working out the solutions on your own. If you have difficulties, you may talk to me or to other students about the homeworks, but you must write up your solutions on your own.

The homeworks will contain a mixture of paper-and-pen exercises and computer exercises. The computer questions can be solved using either MATLAB, Fortran, or C/C++ (your choice). You may talk to other students about the computer exercises, but programs must be done individually.

Exams: One in class midterm, one take home final (collected during finals week). The midterm will probably cover the items 1-3 from the list of topics above.

Grades: Homeworks and the two exams will each count for one third of the grade.

Office Hours: Monday, 12.30-1.30PM, Thursday, 4.0-6.0PM in Amos Eaton 325.

Resources:

• A MATLAB primer: http://www.cs.berkeley.edu/~demmel/ma221/primer4_0_1.ps.gz
• LAPACK: This is a library of numerical linear algebra routines in Fortran and C/C++, available from netlib at http://www.netlib.org

Textbooks:

Required:		Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
			Note that Demmel gives a list of suggested topics for a one-semester course in the preface; I intend to follow this list fairly closely.
			http://www.siam.org/books/demmel/demmel_class
On Reserve:		Golub and Van Loan, Matrix Computations, 3rd edition. Johns Hopkins, 1996.
			Encyclopedic reference.
		Higham, Accuracy and Stability of Numerical Algorithms. SIAM, 1996.
		Trefethen and Bau, Numerical Linear Algebra. SIAM, 1997.
			A good alternative to Demmel.

The World Wide Web: This outline and the homeworks will be available via my homepage,

http://www.rpi.edu/~mitchj/math6800

Academic integrity: Student-teacher relationships are based on mutual trust. Acts which violate this trust undermine the educational process. The Rensselaer Handbook defines various forms of academic dishonesty and procedures for responding to them. The penalties for cheating can include failure in the course, as well as harsher punishments.

Appealing grades: As with any other administrative question regarding this course, see me in the first instance. If we are unable to reach agreement, you may appeal my decision to Professor Holmes

	John Mitchell
	Amos Eaton 325
	276-6915.
	mitchj@rpi.edu