Math 1080:      Numerical Linear Algebra      Spring 2019

Instructor: David Swigon

Office: Thackeray 511, 412-624-4689, swigon@pitt.edu

Lectures:  MWF 10:00-10:50am, Thackeray 524

Office Hours: MW 11:00am-12:30pm, 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 least-square 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 7-11

I.1-2

Matrix Multiplication, Fundamental Theorem

Orthogonality, Euclidean norm

HW 1

Due Jan 18

Jan 14-18

II.6

II.7

Projectors

QR factorization

HW 2

CA 1

Due Jan 25

Jan 21

 

No Class

 

Jan 23-25

II.8

Gram-Schmidt Orthogonalization

HW 3

CA 2

Due Feb 1

Jan 28-
Feb 1

II.10

 

Householder Triangularization,

Householder QR factorization

 

Feb 4

II.11

Applications of QR factorization

HW 4

Due Feb 15

Feb 6

Review (Midterm Exam I Review Topics)

 

Feb 8

Midterm Exam I (Covers Sections I and II)

 

Feb 11-15

III.12

III.13

III.14

Conditioning

Floating point arithmetic

Stability

HW 5

Due Feb 22

Feb 18-22

III.15

III.16

IV.20

Accuracy

Stability of Householder triangularization

Gaussian Elimination

HW 6

CA 3

Due Monday, Mar 4

Feb 25-Mar 1

IV.20

IV.21

Gaussian Elimination (continued)

Pivoting

 

Mar 4 - Mar 8

IV.22

IV.23

Stability of Gaussian Elimination

Cholesky Factorization

HW 7

CA 4

Due Wednesday, Mar 20

Mar 11-15

 

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 25-29

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 8-12

V.28

V.29

I.4

QR Algorithm

QR Algorithm with shifts

Singular Value Decomposition

 

Apr 15-17

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, 412-648-7890, 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 .)

 

E-mail Communication Policy

Each student is issued a University e-mail address (username@pitt.edu) upon admittance. This e-mail address may be used by the University for official communication with students. Students are expected to read e-mail 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 e-mail forwarding service that allows students to read their e-mail via other service providers (e.g., Hotmail, AOL, Yahoo). Students that choose to forward their e-mail from their pitt.edu address to another address do so at their own risk. If e-mail is lost as a result of forwarding, it does not absolve the student from responding to official communications sent to their University e-mail address. To forward e-mail 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 E-mail Communication Policy, go to www.bc.pitt.edu/policies/policy/09/09-10-01.html .)