\documentstyle{article}
\title{CS 594-27550: Iterative Solution of \\ Linear Systems - Fall 1992}
\author{
Instructors: Michael W. Berry (114 Ayres Hall), and \\
June Donato (MSR-ORNL)
}
\begin{document}
\maketitle
\section*{Course Content}
This seminar-based course will focus on the use of popular iterative
methods for the solution of general linear systems of equations. Using
the Stanford University Technical Report NA-91-05 by Freund, Golub,
and Nachtigal as our guide, we will survey Lanczos-based Krylov subspace
methods for the solution of symmetric and nonsymmetric systems.
The first $7$ weeks of the course will comprise a general review
of basic iterative methods (Jacobi, Gauss-Seidel, SOR, etc.,) and
an introduction to well-known Krylov methods (Conjugate Gradient,
Preconditioned Conjugate Gradient, Lanczos, Arnoldi, GMRES, etc.,)
in order to adequately prepare students for
a more detailed study of more recent methods such as CGS, Bi-CGSTAB, and
QMR. Appropriate survey and research papers (plus references) will
be distributed to all registered students during the semester.
\section*{Course Credit}
Students may register for either $1$ or $3$ hours. Students registering
for $1$ hour will be required to make $2$ in-class $10$-$15$ minute presentations
during the semester. Topics for such presentations will be announced by
the instructors periodically.
Students registering for $3$ hours will be required to make $2$
in-class presentations, and choose a course project to present
during the Final Exam week. The project will comprise both
written and oral presentations and will be selected from a list
of topics selected by the instructors. Most projects will involve
programming work to some extent. Topics may be related to the
use of iterative methods in scientific applications or
implementations on parallel computers. The list of topics will be
available before the end of the $7$-week review of iterative methods.
\clearpage
\section*{Grading}
Grades are based on attendance, quality of presentations, and
completeness of the course projects ($3$ hour students only).
Since the class will meet only once per week, students should make
a serious attempt to attend each scheduled meeting.
\section*{Introductory Review}
As mentioned above, this course will begin with a $2$-part overview of
fundamental iterative methods. Part I (2 hours) will cover topics such
as Jacobi, Gauss-Seidel, SOR, matrix splittings, convergence
properties, and acceleration schemes. Part II (2 hours) will
introduce Krylov methods such as Conjugate Gradient, Lanczos, Arnoldi,
and the Generalized Minimum Residual (GMRES) methods.
Other topics presented include preconditioning, optimality, convergence
properties, finite termination, and recurrence relations.
The intent of this review is to re-introduce iterative methods and
to prescribe classical references for outside reading. After
the review, students will be better-prepared to study the
relationships, properties, and applicability of the more recent Krylov
methods proposed for the solution of nonsymmetric linear systems.
\section*{Milestones}
The schedule for the $7$-week review and associated student
presentations\footnote{With $10$ minutes
assigned to each student presentation/lead discussion, we should
be able to have about $15$ presentations during the first $7$ weeks.}
is listed in Table \ref{review}. There will be many opportunities
for in-class presentations after the review, and time to
discuss course projects will also be included throughout the semester.
\begin{table}[hbf]
\begin{center}
\begin{tabular}{|c|c|c|} \hline
Week & Lecture & Student Presentation \\
Number & Hours & Hours \\ \hline
1 & 1.0 & \\
2 & 1.0 & \\
3 & 0.5 & 0.5 \\
4 & & 1.0 \\
5 & 1.0 & \\
6 & 1.0 & \\
7 & & 1.0 \\ \hline
Total & 4.5 & 2.5 \\\hline
\end{tabular}
\end{center}
\caption{Timetable for introductory review\label{review}.}
\end{table}
\section*{Guest Lectures}
During the semester we will have $2-3$ guest lectures by researchers
at UT and ORNL who are experts in the analysis and application of
the iterative methods discussed in this course.
\end{document}