Math 221 Fall 2008, Matrix Computations

General Information

Introduction

Matrix computations are among the most basic of all scientific computations. A surprising number of scientific and engineering problems can be formulated and solved effectively using matrix tools and algorithms. In this course we will introduce numerical methods for solving the three basic problems in matrix computations: linear systems of equations, linear least squares problems, and eigenvalue problems. Along the way, we will also discuss the two most important issues concerning a numerical method, namely speed (or computational efficiency) and accuracy.

Meeting Times

Lectures: MWF 10:00-11:00AM
Classroom: 5 Evans

Staff

Instructor Prof. Ming Gu
Office: 861 Evans
Office Hours: MWF Noon-2:00PM or by appointment.
Phone: 642-3145
Email: mgu@math

Prerequisites

Sufficient knowledge of basic linear algebra concepts and results will be assumed. A working knowledge of matlab is also required. If you wish to take this course but are not sure whether you have met these prerequisites, please contact me. If you have never used matlab before, you can take a look at the Matlab Primer by Kermit Sigmon of the University of Florida.

Textbook

This semester, we will use the text books by J. Demmel: Applied Numerical Linear Algebra, published by SIAM. This is an excellent book covering far more material than we can ever hope to discuss within one semester. Our goal is to cover most of the first five chapters.

There are other excellent reference books in matrix computations as well. Anyone who wants to learn more about it should consult the "Bible": Matrix Computations, 3rd Ed., 1996, Johns Hopkins Press, by G. Golub and C. van, Loan. The book by Trefethen and Bau: Numerical Linear Algebra, published by SIAM, is also an excellent text on the subject.

We plan to cover the first 6 chapters of the Demmel book. We will skip Sections 2.2.1, 2.5.2, 4.5, 5.2.1, 5.5, 6.7, 6.8, 6.9, 6.10.

Numerical Software

There is a great deal of useful information including numerical software on the WWW. In particular, you can get very efficient and reliable software for solving the problems we discuss in class. The following URLs are particularly important in this regard.

Netlib at http://www.netlib.org. Much of free numerical software in common use can be found here, including
- The BLAS routines,
- LAPACK routines,
- Templates for iterative solution of linear system of equations. Iterative methods are usually less reliable than direct methods but much more efficient. They are often the only practical methods for solving large systems of linear equations.
Guide to Available Mathematical Software (GAMS) at http://gams.nist.gov. If you do not know where to look for the numerical software that might solve your problem, this should be a good place to start.

Handouts

This and many other handouts that are distributed in the class can be found at the class home page. From time to time I will also put some matlab codes there.

Course Work and Grading

There are a total of 100 points you can earn toward your final grade in the course.

There will be one midterm exam worth 20 points, and one final exam worth 30 points. Both exams will be cumulative. The midterm exam will be on Monday, Oct. 20, in class, and the final Saturday, December 13, 8:00-11:00AM.

There will be 14 homeworks. Only the best 10, each worth 2 points, will be counted towards the final grade. Some homework sets will be harder than others. They will be a mixture of analytical problems and programming problems, which will mostly be done in matlab . For numerical results, use graphs and plots, instead of tables of numbers, or worse, pages of computer outputs. These graphs and plots are easy to create in matlab. All homeworks will be due on Mondays. I will try to make some solutions available after homework due dates. Most homework problems are from the texts. They are in general good supplement to class material and are fun and/or challenging to solve.

There will also be a list of term projects. Students are strongly encouraged to work on them as groups of up to 3 people. Each group is to work on one project. At the end of the semester, each group is to present their work on their project in front of the whole class. The term project is worth 30 points.

I myself do not have full knowledge of all the issues involved in the projects. We will work together to resolve all the issues involved to the best we can. Some of the topics are still under active attention of the research community. So it should be fun to work on them.

There will be no make-up exams and no late homeworks, unless medical or personal emergencies prevented you from working on them in time.