Math 1080: Numerical Linear Algebra Spring 2019
Instructor: David Swigon
Office: Thackeray 511, 4126244689, swigon@pitt.edu
Lectures:
MWF 10:0010:50am, Thackeray 524
Office
Hours: MW 11:00am12:30pm, Thackeray
511, or by appointment.
Grader: Xing
Wang, Thackeray 623, xiw117@pitt.edu
Course
Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math1080.html
Course
Description
This course
gives an introduction to the basic areas of numerical linear algebra. It will
cover the development and analysis of algorithms that are used in the solution
of linear algebraic equations, algebraic eigenvalue problems and linear
leastsquare minimization problems.
Prerequisites
Basic
knowledge of matrix theory and linear algebra (one of MATH 0250, MATH 0280, or
MATH 1180) plus knowledge of computer programming (one of CS 0002, CS 0007, CS
0401, CS 0132) is expected.
Textbook
L. N. Trefethen & D. Bau III, Numerical
Linear Algebra, SIAM, 1997, ISBN 0898713617
This is a course in applied mathematics and hence
emphasis will be placed on practical usage of methods and algorithms.
Other texts on numerical linear algebra you can use for review of the theory or
for enhancement include:
D. Poole, Linear
Algebra; a Modern Introduction;
G. Strang, Linear
Algebra and Its Applications;
C. G. Cullen, An
Introduction to Numerical Linear Algebra;
C. F. van Loan, Introduction
to Scientific Computing
Grading
Scheme
Homework
assignments: 30%
Two
midterm exams: 20% + 20%
Cumulative
final exam: 30%
Programming
Many
assignments will require computer programming. You are expected to be
proficient in at least one computer language, such as Matlab,
Fortran, C, Basic, JAVA, etc. to such an extent that you can write a program,
debug it, run it, and print out the output. I recommend Matlab, as it makes manipulation of matrices easy and
requires the least coding overhead. Feel free to use your personal computer or
any of the University computing labs to work on your assignments.
Matlab resources
Matlab Primer of Professor Sigmon
of the University of Florida: http://www.math.pitt.edu/~swigon/Matlab/primer.pdf
Matlab documentation: https://www.mathworks.com/help/matlab/
Syllabus
Date 
Reading 
Topics 
Homework

Jan
711 
I.12 
Matrix
Multiplication, Fundamental Theorem Orthogonality,
Euclidean norm 
Due
Jan 18 
Jan
1418 
II.6 II.7 
Projectors
QR factorization 
Due
Jan 25 
Jan
21 

No
Class 

Jan
2325 
II.8 
GramSchmidt
Orthogonalization 
Due
Feb 1 
Jan
28 
II.10 
Householder
Triangularization, Householder
QR factorization 

Feb
4 
II.11 
Applications
of QR factorization 
Due Feb 15 
Feb
6 
Review (Midterm Exam
I Review Topics) 


Feb
8 
Midterm
Exam I (Covers Sections I and II) 


Feb
1115 
III.12 III.13 III.14 
Conditioning
Floating
point arithmetic Stability 
Due
Feb 22 
Feb
1822 
III.15 III.16 IV.20 
Accuracy
Stability
of Householder triangularization Gaussian
Elimination 
Due
Monday, Mar 4 
Feb
25Mar 1 
IV.20 IV.21 
Gaussian
Elimination (continued) Pivoting 

Mar
4  Mar 8 
IV.22 IV.23 
Stability
of Gaussian Elimination Cholesky
Factorization 
Due Wednesday, Mar 20 
Mar
1115 

Spring
Break, No Classes 

Mar
18 
IV.23 
Cholesky
Factorization (continued) 

Mar
20 
Review (Midterm
Exam II Review Topics) 


Mar
22 
Midterm
Exam II (Covers Sections III and
IV) 


Mar
2529 
V.24 V.25 V.27 
Eigenvalue
Problems Overview
of Eigenvalue Algorithms Power
Iteration, Rayleigh Quotient, Inverse iteration 

Apr
1  Apr 5 
V.27 V.26 
Rayleigh
Quotient, Power Iteration, Inverse iteration Reduction
to Hessenberg Form 

Apr
812 
V.28 V.29 I.4 
QR
Algorithm QR
Algorithm with shifts Singular
Value Decomposition 

Apr
1517 
I.5 V.31 
More
on the SVD Computing
the SVD 

Apr
19 
Review
(Final Exam Review Topics) 


FINAL
EXAM 

Disability
Resource Services
If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and the Office of Disability Resources and Services, 140 William Pitt Union, 4126487890, as early as possible in the term. Disability Resources and Services will verify your disability and determine reasonable accommodations for this course.
Academic
Integrity Policy
Cheating/plagiarism will not be tolerated. Students suspected of violating the University of Pittsburgh Policy on Academic Integrity, noted below, will be required to participate in the outlined procedural process as initiated by the instructor. A minimum sanction of a zero score for the quiz, exam or paper will be imposed. (For the full Academic Integrity policy, go to www.provost.pitt.edu/info/ai1.html .)
Email
Communication Policy
Each student is issued a University email address (username@pitt.edu) upon admittance. This email address may be used by the University for official communication with students. Students are expected to read email sent to this account on a regular basis. Failure to read and react to University communications in a timely manner does not absolve the student from knowing and complying with the content of the communications. The University provides an email forwarding service that allows students to read their email via other service providers (e.g., Hotmail, AOL, Yahoo). Students that choose to forward their email from their pitt.edu address to another address do so at their own risk. If email is lost as a result of forwarding, it does not absolve the student from responding to official communications sent to their University email address. To forward email sent to your University account, go to http://accounts.pitt.edu , log into your account, click on Edit Forwarding Addresses, and follow the instructions on the page. Be sure to log out of your account when you have finished. (For the full Email Communication Policy, go to www.bc.pitt.edu/policies/policy/09/091001.html .)