COURSE SYLLABUS

Course Number: MATH7600
Course Title: Advanced Numerical Matrix Analysis 
Credit Hours: 3
Prerequisites: Math6640 or departmental approval
Corequisite: 

Objectives:
This course treats advanced numerical methods for matrix computations. 


Course Content (typical):

Recall of elementary numerical linear algebra  (1 week).

Advanced eigenvalue computations (2 weeks):
Theory of convergence for the QR algorithm; the symmetric QR algorithm; eigenvector computations.

Least squares problems and the singular value decomposition (2 weeks):
Inconsistent linear equations; orthogonal methods; rank deficient least squares; computing the SVD.

Fast matrix techniques (2 weeks):
Fast matrix multiplication; the FFT.

Large scale matrix problems (2 weeks):
Lanczos method for eigenvalues, linear equations and least squares; the conjugate gradient method.

Non--orthogonal matrix eigensolvers (2 weeks):
Theory of DQR algorithm; DQR with shifts; applications to tridiagonal matrices and  polynomial roots.

Stability analysis of matrix algorithms (2 weeks).

Assign around 5 -- 6 programs from the algorithms above to be programmed and 
tested by the students singly or in groups.

Possible Textbooks:} 
J. Demmel, Applied Numerical Linear Algebra, SIAM
G. H. Golub and C. F. van Loan, Matrix Computations, Johns Hopkins University Press
L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM

Sample Grading and Evaluation Procedures

A graduate student is expected to creatively engage the mathematical material of the course.  The student will be given problems to solve; these problems may include the derivation of proofs to theorems.  These solutions may be presented in class on the blackboard or be written up to be handed in to the instructor. Extended projects may also be assigned.  

Grade Calculation
Presentation of solutions to problems/theorems, homework:				40%
Midterm exam or midterm project:							25%
Final Exam or culminating project:							35%

There may be variations in these procedures depending on the individual instructors and the nature of the specific material.
Sample Statement Re: Accommodations
	Students who need accommodations are asked to arrange a meeting during office hours the first week of classes, or as soon as possible if accommodations are needed immediately.  If you have a conflict with my office hours, an alternate time can, be arranged.  To set up this meeting, please contact me by E-mail.  Bring a Copy of your Accommodation Memo and an Instructor Verification Form to the meeting.  If you do not have an Accommodation Memo but need accommodations, make an appointment with The Program for Students with Disabilities, 1244 Haley Center, 844-2096 (V/TT).  (Note: Instructor office room, office hours and email address will be made available on the course syllabus and on the first day of class.)

JUSTIFICATION FOR GRADUATE CREDIT

	This course is part of a modified semester version of a 600-level course under the quarter system.  Under the quarter system it was specifically designed as a graduate course.  It was approved as part of our graduate program and has been a traditional part of our graduate program offerings.  Outside of modernization, the standard of the course remains at the same graduate level that the department has maintained in the past. The course demands considerable mathematics background and a degree of mathematical maturity traditionally found at the graduate level.  The 7000-level course will inculcate the same analytical skills and depth of understanding previously demanded by the comparable 600-level quarter course.  In order to successfully complete the course the student will have to demonstrate an ability to creatively examine and apply the mathematics presented in the course.