TA:
Gabriel Brown
Email: ghbrown@utexas.edu
Office hours: Tuesdays 14:15 - 15:15, Thursdays 11:00 - noon.
Meeting times:
Tuesdays and Thursdays, 9:30 - 10:45. ECJ 1.308
Website:
http://users.oden.utexas.edu/~pgm/Teaching/2024_NLA/
Syllabus:
pdf
Description:
Accurate and efficient algorithms for solving linear algebraic problems form
a cornerstone of scientific and engineering computations.
They are play an essential role in machine learning, data analysis, and computational statistics.
In these areas, tasks such
as solving linear systems, computing eigenvectors and eigenvalues of
large matrices, solving linear regression problems, etc., often form the
core of large scale computations. The class will describe efficient techniques
for solving problems such as these. Both the theoretical
foundations of the methods, and practical considerations for how to implement
the methods efficiently will be covered.
The course will also discuss essential concepts of numerical analysis such as backwards and forwards error analysis, stability of numerical methods, and floating point arithmetic.
Examination:
35% for homeworks, 45% for the section exams (15% for each of the three), 20% for the final exam. See syllabus for details.
Late policy: The first time you hand in a homework late, you will get 70% credit provided that you hand your work in within 5 days of the due date. Any subsequent late homeworks will receive no credit.
Schedule: All future times are tentative!
| Week: |
Homework: |
Material covered: |
| 1 (Aug 26) |
|
Review of basic concepts in linear algebra. Matrix operations (ch 1). Orthonormal matrices (ch 2). |
| 2 (Sep 2) | Homework 1 due on Tuesday Sep 10. |
Vector norms and operator norms (ch 3). SVD (ch 4). The matlab code used in class. |
| 3 (Sep 9) |
|
SVD (ch 5). Projections (ch 6). QR factorization (ch 7). |
| 4 (Sep 16) | Homework 2 due on Sunday Sep 22. |
Gram-Schmidt QR (ch 8). Chapter 9 is part of prereqs. Please review as required. Householder QR (ch 10). Code used in class. Also this. |
| 5 (Sep 23) |
|
Least squares problems (ch 11). The matlab code used in class. Tuesday class conducted via zoom. Section exam 1 in class on Thursday Sep 26. Exam. Solutions. Mean=82. Median=90. |
| 6 (Sep 30) | Homework 3 due on Tuesday Oct 8. |
Least squares problems (ch 11). Conditioning and stability (ch 12-15). |
| 7 (Oct 7) |
|
Conditioning and stability (ch 12-15). The matlab codes, 1 and 2, used in class. |
| 8 (Oct 14) | Homework 4 due on Sunday Oct 20. |
Stability of Householder QR (ch 16 - 17). Stability of least squares problems (ch 18 - 19). LU factorization and solving linear systems (ch 20-23). Codes: LU, LU and pivoting. |
| 9 (Oct 21) |
|
LU factorization and solving linear systems (ch 20-23). Codes: conditioning of LU. Section exam 2 in class on Thursday Oct 24. Exam. Solutions. Mean=78.8. Median=83.5. |
| 10 (Oct 28) | Homework 5 due on Tuesday Nov 5. |
Cholesky factorization (ch 23).
Matlab demo. Computing eigenvalues and eigenvectors. |
| 11 (Nov 4) |
|
Computing eigenvalues and eigenvectors. |
| 12 (Nov 11) | Homework 6 due on Tuesday Nov 19. |
Computing eigenvalues and eigenvectors. Krylov methods and other iterative techniques. |
| 13 (Nov 18) |
|
Krylov methods and other iterative techniques. Sparse direct solvers. Randomized methods. Video lecture on conjugate gradients. (Voluntary!) Video lecture on Krylov for non-normal matrices. (Voluntary!) Video lecture on preconditioners. (Voluntary!) Section exam 3 (take home) due on Wednesday Dec 4, at noon. Code for exam 3. Matrix Y in problem 4: matlab, plain text. |
| (Nov 25) |
|
Thanksgiving this week. No classes. However, you are welcome to join me at these times: Monday 9:30 - 10:45: Review lecture 1 (zoom). Tuesday 9:30 - 10:45: Review lecture 2 (zoom). |
| 14 (Dec 2) |
|
Tue: Review - video recorded lecture.
No regular class! Thu: Review - video recorded lecture. No regular class! |
| 16 (Dec 9) |
|
Final exam on Friday Dec 13, 10:30am - 12:30pm. |
Resources: