Numerical Linear Algebra, CMSE 823
|Time and Place:||Lectures are Tu Th 8:30 am -- 9:50 am, in B104 Wells Hall|
|Office Hours:||Tu 10:00 am -- 11:00 am, and Th 10:00 am -- 11:00 am|
This course will cover numerical methods for efficiently solving linear equations and eigenvalue problems. Emphasis will be on the design and analysis of efficient and stable numerical schemes. Students will learn how to solve least squares problems, how to numerically approximate eigenvalues/eigenvectors of matrices, how to compute fundamental matrix factorizations (LDU, SVD, QR, Cholesky, ...), and how to determine the best numerical method to use for doing all of these based on the characteristics of a given linear system (repeated eigenvalues, ill-conditioned systems, etc.). In order to understand why specific methods will or won't work in specific settings, we'll also need some basic knowledge of matrix analysis (e.g., matrix norms, condition numbers, basic perturbation theory).
Course website for CMSE 823-001:
The course website is mandatory reading for the course. On it you will find the course schedule, the syllabus, and supplementary reading. Homework assignments will be posted on the schedule.
Numerical Linear Algebra, by Lloyd N. Trefethen and David Bau III.
The majority of the course will be spent covering this book from cover to cover.
We will also utilize material from the following books, all of which are highly recommended (but not required):
- Applied Numerical Linear Algebra, by James W. Demmel.
- Matrix Analysis (2nd edition), by Roger A. Horn and Charles R. Johnson.
Cambridge University Press, 2013.
- Matrix Perturbation Theory, by G. W. Stewart and Ji-guang Sun.
Academic Press Inc., 1990.