Who: Taught by Amit Chakrabarti;
teaching assistant: Hao Luo When: 2 hour, MWF 13:45-14:50, X-hr Th 13:00-13:50 Where: Sudikoff 214 Office hours: Amit: Mon & Fri 10:30-11:30 in Sudikoff 107;
Hao: Tue 14:00-15:00 in Sudikoff 114 This course is about how to solve, computationally, linear algebra
problems. "Numerical analysis is the study of algorithms for the problems of continuous mathematics." Please read the Appendix of the text book before the second class for a much more insightful and thorough discussion about what this course is about. Textbook: -
**Main text:**L. N. Trefethen and D. Bau.*Numerical Linear Algebra*, SIAM, 1997. - We might also use supplementary material.
Syllabus: This is a rough and tentative syllabus, essentially copied from the textbook. - orthogonal vectors, norms, singular value decomposition
- QR factorization, Gram-Schmidt orthogonalization, and least squares problems
- conditioning and stability
- Gaussian elimination and Cholesky factorization
- eigenvalue problems, Raleigh quotient, QR algorithm
- iterative methods: Arnoldi, Lanczos, conjugate gradient
- preconditioning
Prerequisites: - Familiarity with linear algebra and with computers
- Mathematical maturity
Workload and Grading: - 60% Weekly homework assigments: a mix of problem solving, writing mathematical proofs, and programming in Matlab.
- 15% Midterm exam: in class, starting at the X-hour on Thu Oct 28, 2010. Details and rules here.
- 25% Final exam: take home,
self-timed exam (due by 3:00pm on Dec 8, 2010)
You may read the instructions on page 1, but do not look at any other pages until you are ready to start the exam!
Homework: In general, homework will be due each Wednesday before class. You may submit by either bringing it to me (Amit) in class, or putting it in my mailbox. - HW 1, due Wed Sep 29, before class
- HW 2, due Wed Oct 6, before class
(Matlab is available on department Unix servers and 0^{th}Floor machines, plus you can download it) - HW 3, due Wed Oct 13, before class
- HW 4 due Wed Oct 20, before class
- HW 5 due Wed Oct 27, before class
- HW 6 due Fri Nov 5, before class
- HW 7 due Fri Nov 12, before class
- HW 8 due Fri Nov 19, before class
- HW 9
(details added, submission deadline extended),
due Wed Dec 1, before class
References, for further reading: - The now-classic textbook
*Matrix Computations*, by Golub and van Loan has lots of technical detail that our textbook doesn't. - For plenty more detail on backward errors and condition numbers for least squares problems, refer to the very detailed report "Optimal Sensitivity Analysis of Linear Least Squares", by Joseph F. Grcar.
- For more on smoothed analysis of Gaussian Elimination, with and without pivoting, refer to "Smoothed Analysis of Gaussian Elimination", the Ph.D. Thesis (MIT, 2004) of Arvind Sankar.
- Jonathan Shewchuk's 1994 paper An Introduction to the Conjugate Gradient Method Without the Agonizing Pain is a good read, despite the exaggerated negativity of the title.
Last updated Oct 29 2010 |