Numerical Linear Algebra
MATH 432
MWF 1:30-2:20 pm, TLC 247
Instructor:
|
Lyudmyla Barannyk
317 Brink Hall
tel: (208) 885-6719
fax: (208) 885-5843
barannyk@uidaho.edu
office hours:
M,W 3:30-4:30 pm, Th 4:30-5:30 pm
or by appointment
|
There is a class email list: math432-f13@uidaho.edu.
You can make an alias for it. You can use the email list to ask me
questions that might be of interest to others in the class. You can
also email me at barannyk@uidaho.edu
with other questions.
Course Description
Math 432 is an introduction to numerical linear algebra, a core subject
in scientific computing. Three types of problems are considered: (1)
solving a system of linear equations (Ax=b), (2) computing eigenvalues
and eigenvectors of a matrix (Ax=\lambda x), and (3) least squares
problems (min ||Ax - b||_2). These problems arise in applications in
science and engineering, and many methods have been developed for their
solution, but standard
methods may fail if the problem is large or ill-conditioned, e.g. the
operation count may be prohibitive or computer roundoff may ruin the
answer. We’ll investigate these issues and study some of the accurate,
efficient, and stable methods that have been devised to overcome these
difficulties.
Textbook
Numerical Linear Algebra and Applications
by B.N. Datta, SIAM, 2010
MATCOM programs can be found here: http://www.siam.org/books/ot116/
Additional reading:
Fundamentals of Matrix Computations
by D. Watkins, Wiley, 2010, QA188.W38 2010
Numerical Linear Algebra by
L.N. Trefethen and D. Bau III, SIAM, 1997, Internet QA184.T74
1997
Applied Numerical Linear Algebra
by J.W. Demmel, SIAM, 1997, Internet QA184.D455 1997
Numerical Methods An Introduction
to
Scientific Computing Using Matlab by Peter Linz and Richard L.C.
Wang
Conjugate Gradient Method (Burden &
Faires)
Iterative methods for linear systems
(Bradie)
Numerical Computing with MATLAB by Cleve B. Moler
ISBN: 0898715601, Society for Industrial & Applied (06/01/2004)
Available electronically at http://www.mathworks.com/moler/
A Friendly Introduction to Numerical Analysis by Brian Bradie,
ISBN: 0-13-013054-0, Prentice Hall, 2006
Selected programs: http://www.pcs.cnu.edu/~bbradie/matlab.html
Selected solutions/answers: http://www.pcs.cnu.edu/~bbradie/textbookanswers.html
Numerical Methods Using Matlab (Fourth Edition).
By: John H. Mathews and Kurtis D. Fink
Errata for 4th Edition: Numerical
Methods Using MATLAB, John H. Mathews and Kurtis D. Fink
An
introduction to
numerical analysis
By: Kendall E. Atkinson
QA 297.A841
Numerical Analysis
By: Richard L. Burden and J. Douglas Faires
Elementary Numerical Analysis (3rd
Edition)
By: Kendall Atkinson and Weimin Han
MATLAB guide
By: Desmond J. Higham & Nicholas J. Higham.
QA297 .H5217 2000
Syllabus
Download syllabus: .pdf
Learning Outcomes
- Students will be introduced to modern concepts and
methodologies of numerical linear algebra including various
factorizations, iterative methods and their analysis, that can be used
to solve linear algebra problems arising in many applications in
physics and engineering.
- Students will learn theoretical aspects such as stability and
convergence that will enhance their understanding of the numerical
methods.
- Students will be able to select or design a method or approach
for solving a problem in numerical linear algebra; evaluate a method
for its accuracy, stability, and computational cost; and discuss
efficiency implications in a computer implementation of a method,
including parallel computing aspects.
- Students will gain experience in implementing and observing the
numerical performance of the various numerical methods using Matlab.
-
Computer language
In this course, we will make extensive use of Matlab, a technical
computing environment for numerical computation and visualization
produced by The MathWorks, Inc.
This will take a little learning, but will pay off in the
long
run, since programming numerical methods is much easier (and quicker)
in
Matlab than in virtually any other language.
A Matlab manual is
available in the MSCC Lab.
Also available is a MATLAB
tutorial written by
Peter Blossey: (.pdf)
Another
standard
one is Kermit Sigmon's Matlab Primer:
(.html)
Here is another Matlab resource available on the net:
In addition, there are many textbooks about Matlab. One of them is
MATLAB guide
By: Desmond J. Higham & Nicholas J. Higham.
QA297 .H5217 2000
Handouts
in
format
Lecture Notes
Schedule, Homework and Exams
Follow links in the table below to obtain a copy of the
homework in 
Adobe Acrobat(.pdf)
format.
| Homework Sets |
Due Date
|
hw1
|
Friday, September
6
|
hw2
|
Friday, September
13 |
hw3
|
Friday, September
20 |
|
hw4 |
Friday, September
27 |
|
hw5 |
Friday, October 4
|
hw6
|
Friday, October
11 |
hw7
|
Friday, November
1 |
hw8
|
Friday, November
8 |
|
hw9 |
Friday, November
15 |
|
hw10 |
Friday, November
22 |
|
hw11 |
Friday, December
6 |
|
hw12 |
Friday,
December 13
|
Midterm:
Friday, October 11 in class
Midterm
Review: October 10, 4:30-5:30 pm, TLC 245 review notes
Final:
Tuesday, December 17, 12:30 - 2:30 pm, TLC 247
Final Review: TBA
Grading
40%- Homework
25%- Midterm Exam
35%- Final Exam
Midsemester Questionnaire