CSE/MATH-6643 — Numerical Linear Algebra
Instructor Information
Lectures: M W 8:00-9:15am
Location: TSRB 132
Instructor: Qi Tang
Email: qtang@gatech.edu
Office Hours: TBD via zoom
TA: TBD
Email: TBD
Office Hours: TBD
Course Description
This course introduces fundamental algorithms in numerical linear algebra, including methods for solving linear systems, constructing orthogonal bases, and computing eigenvalue and singular value decompositions (SVD).
A key objective is to prepare Ph.D. students for the qualifying exam; therefore, the course emphasizes theorems, proofs, and the mathematical principles underlying these algorithms.
Prerequisites
- MATH 2406 or MATH 4305
- MATH 4640 is not required but strongly recommended
Topics
- Problem conditioning, perturbation theory
- Stability, error analysis
- Floating point computation, parallel computation
- Computational complexity of algorithms
- SVD, QR, and other orthogonal factorizations
- Solving linear least squares problems, including rank deficient problems
- Gaussian elimination
- Iterative methods and their convergence for solving linear systems (Jacobi, Gauss-Seidel, etc.)
- Eigenvalue problems and their solution (symmetric and nonsymmetric)
- Krylov subspace methods for eigenvalues and linear systems (Lanczos, Arnoldi, CG, GMRES)
Grading
The weights for the course grade are as follows. Students must score at least 50% on the final exam to pass the course.
| Category | % |
|---|---|
| Homework | 30% |
| Midterm | 30% |
| Final | 40% |
The final course grade will be assigned based on the following scale. Scores are rounded to the nearest integer.
| Grade | % |
|---|---|
| A | 90-100% |
| B | 80-89% |
| C | 70-79% |
| D | 60-69% |
| F | 0-59% |
Pass/Fail
For pass/fail, the passing grade is 50% overall. You are strongly encouraged to attend class regularly.
Textbooks
- Numerical Linear Algebra, Trefethen and Bau.
This is a very clearly written textbook, and we will cover the entire book. You can order this book from SIAM. You can get a 30 percent discount if you are a SIAM member. As a student, you can join SIAM for free, since Georgia Tech is an Academic Member.
Additional References:
- Matrix Computations, Golub and Van Loan. This is the bible of numerical linear algebra.
- Applied Numerical Linear Algebra, Demmel.
- Numerical Linear Algebra with Julia, Darve and Wootters.
- The Matrix Cookbook, Petersen and Pedersen. This online book contains many important identities and is incredibly useful.
Homework Policy
All homework is due by the EOD (11:59pm).
You have a pool of 72 penalty-free late hours for the whole term, which you may spend across all the assignments however you choose. Once that buffer is used up, homework is penalized by 20% for each day it is late; any partial day counts as a full day. The penalty is additive, so no credit is given after five late days.
We strongly encourage the use of LaTeX for your submission. Unreadable handwriting is subject to zero credit.
Class Management
We will use Canvas to deliver course materials and announcements.
Course Policies, Expectations & Guidelines
Plagiarism & Academic Integrity
Georgia Tech aims to cultivate a community based on trust, academic integrity, and honor. Students are expected to act according to the highest ethical standards. For more information on the Honor Code, please visit the OSI website.
We encourage you to discuss course content and homework problems with your classmates. However, all answers and code should be prepared independently. If you refer to any material, it should be properly cited. Needless to say: you are not allowed to use solutions to homework problems that you may find online. If you discussed homework problems with your classmates, indicate which problems you discussed with whom.
Any student suspected of cheating or plagiarizing on an exam or assignment will be reported to the Office of Student Integrity, which will investigate the incident and identify the appropriate penalty for violations.
Role of AI Assistants
The use of LLMs like ChatGPT and Gemini will be treated like a human collaborator: you have to indicate their use and what you used them for. You may only use them to get ideas or to get unstuck on a problem. Like a human collaborator, you should not use LLMs when preparing your solutions or code. For instance, directly copying the output of a chatbot is strictly forbidden.
Accommodations for Individuals with Disabilities
If you are a student with learning needs that require special accommodation, contact the Office of Disability Services at (404) 894-2563 or website, as soon as possible, to make an appointment to discuss your special needs and to obtain an accommodations letter. Please also email me as soon as possible in order to set up a time to discuss your learning needs.
Student-Faculty Expectations
The Georgia Tech community believes that it is important to continually strive for an atmosphere of mutual respect, acknowledgement, and responsibility between faculty members and the student body. See here for the specific expectations of each side.