CSE/MATH-6644
Iterative Methods for Systems of Equations
Instructor Information
Lectures: M W 2:00-3:15pm
Location: Skiles 271
Instructor: Qi Tang
Email: qtang@gatech.edu
Office Hours: T 2-3pm via zoom
TA: Huizhong Xue
Email: hxue32@gatech.edu
Office Hours: F 2-3pm at KACB 3121.
Course Description
This class covers a wide range of iterative methods for solving linear and nonlinear systems of equations. Among the topics covered are fixed-point iterations, splitting methods, Krylov subspace methods, (multigrid) preconditioners, and Newton-type methods. The class will present the mathematical underpinnings of these methods and use them, together with numerical experimentation, to study their properties. Some programming exercises will be assigned, and students may use any programming language of their choice.
Prerequisites
- MATH 2406, MATH 4305 and MATH 4640
- CSE/MATH 6643 is not required but strongly recommended
Grading
The weights for the course grade are as follows. There is no final exam.
| Category | % |
|---|---|
| Homework (4 sets) | 75% |
| Final project | 20% |
| Attendance and participation | 5% |
Each of the four homework sets is worth 18.75%. The final project is broken into three graded components: proposal (2.5%), presentation (2.5%), and written report (15%).
Attendance and participation are assessed holistically: regular attendance together with engagement in class. There is no sign-in sheet and no fixed formula.
The final course grade will be assigned based on the following scale.
| Grade | % |
|---|---|
| A | 90-100% |
| B | 80-89% |
| C | 70-79% |
| D | 60-69% |
| F | 0-59% |
Pass/Fail and Audit
For pass/fail, the passing grade is 50% and you are strongly encouraged to attend class regularly. If you wish to take the course for audit credit, the audit credit is given for a grade of at least 20% and you are strongly encouraged to attend class regularly.
Textbooks
- Iterative Methods for Sparse Linear Systems, Yousef Saad
- Numerical Optimization, Nocedal and Wright
- Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Dennis and Schnabel
- Solving Nonlinear Equations with Newton's Method, Kelley
- Matrix computations, Golub and Van Loan
Additional References:
- 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 the four assignments however you choose. Once that buffer is used up, homework is penalized by 20% for each day it is late (this applies additively, meaning that no credit is gained after five late days).
We strongly encourage the use of LaTeX for your submission. Unreadable handwriting is subject to zero credit. Include the code you used and the relevant output, not just your final results.
Class Management
We will use Canvas to deliver course materials and announcements.
Lectures are in person. A few lectures will be recorded and posted on Canvas when the instructor is travelling; this will be announced at least one week in advance.
Final Project
The final project will allow you to focus more on a topic of particular interest in groups of two to three students. You are encouraged to be creative and develop your own questions to investigate. For instance, you could propose and study a new modification for an existing algorithm, explore an interesting application of an existing algorithm, or explore an aspect that was not covered during class.
The project is graded in three parts: a short proposal (2.5%) setting out the question, the method, and how you will evaluate it; a presentation to the class at the end of the term (2.5%); and a written report (15%) containing your analysis, code, and results.
For the project you are also allowed to build on established libraries such as PETSc, hypre, and MFEM.
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 codes 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 a quiz, 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
You are responsible for everything you submit. You may use LLMs like ChatGPT, Claude and Gemini while you work — for ideas, for getting unstuck, and to help draft your solutions and code — but you must understand and be able to verify every line that carries your name.
Three conditions apply:
- Disclose. Indicate that you used an LLM and what you used it for.
- Understand. You must be able to explain every line you submit, reproduce it, and defend it if asked.
- Verify. Check the output for correctness. An LLM will produce plausible mathematics that is wrong.
Submitting anything you cannot explain, or have not checked, is considered cheating. The same standard applies to material from any other source: cite it, understand it, and be able to stand behind it.
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. Therefore, we herein endeavors to enumerate the specific expectations of each side. See here for more details.