1. Announcements
- Sep 3:
The first lecture will take place on Thursday, September 5.
- Sep 20:
Assignment 1 is posted, due Oct. 10th.
- Sep 20:
There are no lectures on Sept. 23, 25; there are make-up lectures
on Oct. 11, 18, 11-12, ICCS 206.
2. Calendar
| Date |
Lecture contents |
Suggested reading |
|---|
| 5 Sep |
Introduction |
Saad Chapter 1 |
| 10 Sep |
Finite difference discretizations |
Saad Chapter 2 |
| 12 Sep |
Saddle-point systems |
Benzi, Golub and Liesen |
| 17 Sep |
Stationary methods |
Lecture notes, pages 1-5 |
| 19 Sep |
Introduction to nonstationary methods |
Lecture notes, pages 5-8 |
| 1 Oct |
Projection methods |
Lecture notes, pages 10-12; Saad, Chapter 5 |
| 3 Oct |
Arnoldi and Lanczos |
Lecture notes, pages 12-15 |
| 8 Oct |
MINRES, GMRES, CG |
Lecture notes, pages 17-18 |
| 10 Oct |
Preconditioning: introduction |
Saad, Chapter 9 |
| 11 Oct |
Preconditioning: incomplete factorizations |
Saad, Chapter 10, Sections 10.3 and 10.4 |
| 15 Oct |
GMRES: the gory details |
Saad, Section 6.5 |
| 17 Oct |
CG: the gory details; Intro to Multigrid |
Demmel Chapter 6, Multigrid Tutotial
|
| 22 Oct |
Guest lecture, Eldad Haber: multigrid |
live coding and other treats
|
| 24 Oct |
Algebraic multigrid |
Multigrid Tutorial, Chapter 8
|
| 29 Oct |
Bi-Conjugate methods |
Saad, Chapter 7
|
| 31 Oct |
Direct methods: graphs, RCM |
Saad, Sections 3.1-3.3, my slide 1
|
| 5 Nov |
Direct methods: Minimum Degree |
Amestoy, Duff, and Davis; my slides 2-6
|
| 7 Nov |
Direct methods: Approximate Minimum Degree |
Amestoy, Duff, and Davis; my slides 7-10
|
| 12 Nov |
Eigenvalue problems: power and inverse power |
Demmel, Chapter 4
|
| 14 Nov |
Orthogonal iteration, QR iteration |
Demmel, Chpater 4
|
| 19 Nov |
Implicitly restarted Arnoldi |
Saad eig. book Chapter 7
|
| 21 Nov |
Jacobi-Davidson |
Hochstenbach and Notay paper
|
| 26 Nov |
Saddle-point systems preconditioning |
Slides
|
| 28 Nov |
The greatness of matrix computations |
An emotional speech
|
3. Course
Material
Click here
(password protected)
4. Course Overview
Formulation and analysis of algorithms for sparse matrices; direct and
iterative solvers for sparse linear systems; eigenvalue problems;
least-squares problems; applications.
Detailed Outline (click here)
Instructor. Chen Greif,
ICCS 219, greif@cs.ubc.ca.
Office hours.
Thursday, 3:30-4:30, ICCS 219, or by appointment.
Prerequisites. Basic
background in linear algebra and numerical methods.
Drop by to consult with the instructor if unsure.
Intended audience. Beginning or
advanced graduate students
specializing in computer science, mathematics, physics, geophysics, or engineering.
Suggested readings. There is
no required textbook for this course. Useful texts are:
- Uri Ascher and Chen Greif, A First
Course in Numerical Methods (SIAM, 2011)
- Tim Davis,
Direct Methods for Sparse Linear Systems (SIAM, 2006)
- Jim Demmel,
Applied Numerical Linear Algebra (SIAM, 1997)
- Gene Golub and Charles Van Loan,
Matrix Computations (Johns Hopkins, 2012)
- Yousef Saad,
Iterative Methods for Sparse Linear Systems (SIAM, 2003)
- Nick Trefethen and David Bau,
Numerical Linear Algebra (SIAM, 1997)
Homework. There will be a few assignments throughout the term.
You may collaborate and consult with other students in the course, but you must hand in your own
assignments and your own code.
All homeworks involve programming tasks in Matlab.
Course project.
The project typically includes a written summary, computer code, and an oral presentation of your work on a research paper relevant to the material covered in the course.
Grading scheme (tentative).
Your grade
will be determined approximately by the following scheme:
- assignments: approximately
a third of your grade
- project: approximately two thirds of your grade
The instructor reserves the right to modify the grading scheme if
it becomes necessary.
5. Links and Resources
Matlab is a product of Mathworks. Their own guides can be found on their
website.
A couple of other resources, with many additional links:
The Scientific Computing Laboratory
The Scientific Computing and Applied & Industrial Mathematics group at UBC (SCAIM).