Math 1080: Numerical Linear Algebra Spring 2011
Instructor: David Swigon
Office: Thackeray 511, 412-624-4689, swigon@pitt.edu
Lectures: MWF 11:00-11:50am, Thackeray 627
Office Hours: MW 2:00-3:00pm, Thackeray 511, or by appointment.
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 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
G. Golub and C. van Loan, Matrix Computation
Grading Scheme
Homework assignments: 30%
Two midterm exams: 20% + 20%
Final exam: 30%
Schedule
The precise schedule and a list of homework problems will be given out in advance and posted on the web. Homework is due in the beginning of a class one week after it was assigned. You may work with other students on homework but solutions that are identical copies of each other will be discarded.
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 numerical subroutine, debug it, run it and print out the output. I personally recommend Matlab as it makes manipulation of matrices easy and requires the least coding overhead.
You can use 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: http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html
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 Disability Resources and Services, 140 William Pitt Union,
412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will
verify your disability and determine reasonable accommodations for this course.
Academic
Integrity
Cheating/plagiarism will not be tolerated.
Students suspected of violating the University of Pittsburgh Policy on Academic
Integrity will incur a minimum sanction of a zero score for the quiz, exam or
paper in question. Additional sanctions may be imposed, depending on the
severity of the infraction. On homework,
you may work with other students or use library resources, but each student
must write up his or her solutions independently. Copying solutions from other
students will be considered cheating, and handled accordingly.
Syllabus
|
Date |
Reading |
Topics |
Homework |
|
Jan 5 |
I.1-2 |
Matrix Multiplication, Orthogonality, |
|
|
Jan 7 |
I.3, II.6 |
Norms, Projectors |
Due Jan 14 |
|
Jan 10 |
II.7 |
QR factorization |
|
|
Jan 12 |
II.7 |
QR factorization (cont’d) |
|
|
Jan 14 |
II.8 |
Gram-Schmidt Orthogonalization |
Due Jan 21 |
|
Jan 17 |
|
No Class |
|
|
Jan 19 |
II.8 |
Gram-Schmidt Orthogonalization (cont’d) |
|
|
Jan 21 |
II.10 |
Householder Triangularization |
|
|
Jan 24 |
II.10 |
Householder QR factorization |
Due Jan 31 |
|
Jan 26 |
II.10 |
Comparison of Gram-Schmidt and Householder algorithms |
|
|
Jan 28 |
II.11 |
Applications of QR factorization |
|
|
Jan 31 |
Review |
||
|
Feb 2 |
Midterm Exam I |
||
|
Feb 4 |
III.12 |
Conditioning |
|
|
Feb 7 |
III.13 |
Floating point arithmetic |
|
|
Feb 9 |
III.14 |
Stability |
|
|
Feb 11 |
III.15 |
Accuracy |
Due Feb 18 |
|
Feb 14 |
III.16 |
Stability of Householder triangularization |
|
|
Feb 16 |
III.17 |
Stability of Back Substitution |
|
|
Feb 18 |
IV.20 |
Gaussian Elimination |
Due Feb 25 |
|
Feb 21 |
IV.20 |
Gaussian Elimination (cont’d) |
|
|
Feb 23 |
IV.21 |
Pivoting |
|
|
Feb 25 |
IV.21 |
Pivoting (cont’d) |
Due Mar 4 |
|
Feb 28 |
IV.22 |
Stability of Gaussian Elimination |
|
|
Mar 2 |
IV.23 |
Cholesky Factorization |
|
|
Mar 4 |
IV.23 |
Cholesky Factorization (cont’d) |
Due Mar 16 |
|
Mar 7-11 |
|
Spring Break – No Classes |
|
|
Mar 14 |
IV.23 |
Cholesky Factorization (cont’d) |
|
|
Mar 16 |
Review |
||
|
Mar 18 |
Midterm Exam II Covers Lectures of Feb 4 – Mar 14 |
||
|
Mar 21 |
V.24 |
Eigenvalue Problems |
|
|
Mar 23 |
V.24 |
Eigenvalue Problems (cont’d) |
|
|
Mar 25 |
V.25 |
Overview of Eigenvalue Algorithms |
Due Apr 1 |
|
Mar 28 |
V.26 |
Reduction to Hessenberg Form |
|
|
Mar 30 |
V.27 |
Rayleigh Quotient, Power Iteration |
|
|
Apr 1 |
V.27 |
Inverse iteration |
Due Apr 8 |
|
Apr 4 |
V.28 |
QR Algorithm |
|
|
Apr 6 |
V.28 |
QR Algorithm (cont’d) |
|
|
Apr 8 |
V.29 |
QR Algorithm with shifts |
Due Apr 15 |
|
Apr 11 |
I.4 |
Singular Value Decomposition |
|
|
Apr 13 |
I.5 |
More on the SVD |
|
|
Apr 15 |
V.31 |
Computing the SVD |
Due Apr 22 |
|
Apr 18-22 |
Review |
|
|
|
Apr 27 |
|
FINAL EXAM 8-9:50am Thack 627 |
|