Math 614 Numerical Linear Algebra

Fall 2015, UAF

Instructor: Ed Bueler

Office: Chapman 301C.
Phone: 474-7693
eMail: elbueler@alaska.edu

Class Times & Room: MWF 9:15--10:15 Bunnell 410
CRN: 78256
Text: Trefethen & Bau, Numerical Linear Algebra, SIAM Press 1997

Course Web Site: bueler.github.io/M614F15/index.html

Ed's schedule and Office Hours: bueler.github.io/OffHrs.htm

Course Content and Goals:

This course covers how actual matrices and vectors are handled in a fast and accurate manner. This essential technology for scientific and engineering computation will be placed in the correct framework, emphasizing the geometry of the matrix action. Central themes are the conditioning of problems and the stability of algorithms. We will cover famous matrix decompositions, theorems, and algorithms: singular value decomposition (SVD), LU decomposition, spectral theorem, Schur decomposition, the QR method for eigenvalues, and Krylov methods.

Applications of these ideas include solving large linear systems, solving systems of ordinary differential equations, statistical methods, inverse methods in geophysics, and Markov processes. Numerical linear algebra is key for numerically solving partial differential equations, network problems, and optimization problems.

Examples in class will often use Matlab/Octave. (Or python+scipy=pylab for students who are already comfortable with python.) I will help students learn how to use one of these tools, all of which are well-suited to numerical linear algebra. Student competence with such a language, for scientific computing though not necessarily general computer programming, is a goal of the course.

Topics:

matrix/vector mechanics
geometric view of linear algebra
singular value decomposition
QR factorization and least squares
conditioning and stability
operation count and problem size
systems of equations and Gaussian elimination
computing eigenvalues
iterative methods

Outcomes:

At the end of this course you will be able to understand and apply the ideas and algorithms of numerical linear algebra. You will be very comfortable with Matlab or a similar language.

Assigned Work, Evaluation, and Grading:

Weekly homework dominates your grade. The homework will include by-hand computations, proofs, and Matlab/Octave computations. There will also be a one hour in-class midterm exam, emphasizing definitions and basic manipulations, and a take-home final exam emphasizing proofs and nontrivial calculations/applications.

Work
Homework
In class Midterm Exam
Take home Final Exam

Percent of Grade
55%
20%
25%

Dates
nearly weekly
Friday, 30 October, in class
Due in my box 5:00 p.m., Wed., Dec. 16.

Based on your raw homework and exam scores, I guarantee grades according to the following schedule: 90 - 100 % = A, 79 - 89 % = B, 68 - 78 % = C, 57 - 67 % = D, 0 - 56 % = F. I reserve the right to increase your grade above this schedule based on the actual difficulty of the work and on average class performance.

Policies:

The Dept of Mathematics and Statistics has reasonable policies on incompletes, late withdrawals, early final examinations, etc.; see www.uaf.edu/dms/policies. You are covered by the UAF Student Code of Conduct. I will work with the Office of Disabilities Services (208 WHIT, 474-5655) to provide reasonable accommodation to student with disabilities.

Prerequisites:

Undergraduate linear algebra and mathematical maturity. Concretely, MATH 314 Linear Algebra or equivalent. Recommended: MATH 421 Applied Analysis OR MATH 401 Introduction to Real Analysis OR equivalent post-calculus course in analysis.